Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions

Juan Pablo Vielma
Juan Pablo Vielma
[email protected]
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Search for more papers by this author
,
Shabbir Ahmed
Shabbir Ahmed
[email protected]
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Search for more papers by this author
,
George Nemhauser
George Nemhauser
[email protected]
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Search for more papers by this author

Juan Pablo Vielma

[email protected]

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Search for more papers by this author

Shabbir Ahmed

[email protected]

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Search for more papers by this author

George Nemhauser

[email protected]

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Search for more papers by this author

Published Online:28 Oct 2009https://doi.org/10.1287/opre.1090.0721

Supplemental Material

opre.1090.0721-sm-ec.pdf (246 KB)

Cited by
- Route choice behaviour and lane management strategy considering capacity variability for mixed flow of autonomous vehicles
  29 January 2026 | Transportmetrica B: Transport Dynamics, Vol. 14, No. 1
- Optimal design of a low-carbon concrete production plant considering variable material composition and electricity prices
  Computers & Chemical Engineering, Vol. 213
- On the Approximation of Separable Nonconvex Optimization Programs to an Arbitrary Numerical Tolerance
  Claudio Contardo,
  Sandra U. Ngueveu
  19 June 2026 | INFORMS Journal on Computing, Vol. 0, No. 0
- Design and Optimization of Supply Chain for Citrus Biorefineries: A Regional Approach for Waste Valorization in Brazil
  19 June 2026
- From calibrated risk to actionable response: A prescriptive analytics pipeline for urban flash floods
  Resilient Cities and Structures, Vol. 5, No. 2
- P-V2B: A Neuro-Symbolic Framework for Leveraging User Persistence in Vehicle-to-Building Charging
- Global optimization of space mission concept of operations and systems design via mixed-integer nonlinear programming
  Acta Astronautica, Vol. 242
- Degradation-Aware Stochastic Scheduling of Multi-Stack Power-to-X Plants Under Joint Renewable and Electricity Price Uncertainty
  21 May 2026 | Energies, Vol. 19, No. 10
- A Relax-Fix-and-Exclude algorithm for an MINLP problem with multilinear interpolations
  28 February 2026 | Journal of Global Optimization, Vol. 94, No. 4
- Expediting global optimization of gas transport networks with difference-of-convex continuous piecewise linear surrogates
  Journal of Process Control, Vol. 160
- Optimizing representation in redistricting: dual bounds for partitioning problems with non-convex objectives
  30 March 2026 | Mathematical Methods of Operations Research, Vol. 62
- When Deep Learning Meets Polyhedral Theory: A Survey
  Joey Huchette,
  Gonzalo Muñoz,
  Thiago Serra,
  Calvin Tsay
  12 March 2026 | INFORMS Journal on Computing, Vol. 0, No. 0
- Spatial Branch-and-Bound for Nonconvex Separable Piecewise Linear Optimization
  Thomas Hübner,
  Akshay Gupte,
  Steffen Rebennack
  27 June 2025 | INFORMS Journal on Computing, Vol. 38, No. 2
- Improving real-world execution of optimized trading schedules for large-scale battery storage systems through data-driven component parametrization
  Applied Energy, Vol. 407
- Coupled optimization of hydropower and variable renewable energy (VRE) synergistically supported by physically-based stochastic scenarios and multi-load node control
  Energy, Vol. 346
- Building Formulations for Piecewise Linear Relaxations of Nonlinear Functions
  Bochuan Lyu,
  Illya V. Hicks,
  Joey Huchette
  24 April 2025 | Operations Research, Vol. 74, No. 1
- Optimization Over Trained (and Sparse) Neural Networks: A Surrogate Within a Surrogate
  1 June 2026
- Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms
  1 June 2026
- Computing approximate Nash equilibria for integer programming games
  31 July 2025 | Optimization Letters, Vol. 20, No. 1
- Reinforcement learning-guided two-stage optimization framework for multi-product batch scheduling
  Computers & Chemical Engineering, Vol. 204
- Tightening the Difference-of-Convex Formulation for the Piecewise Linear Approximation in General Dimensions
  Quentin Ploussard,
  Xiang Li,
  Matija Pavičević
  29 December 2025 | INFORMS Journal on Optimization, Vol. 0, No. 0
- Medium to long-term optimization model and scheduling strategy for cascade hydropower plants under high penetration of variable renewable energy
  Renewable Energy, Vol. 254
- Short-term scheduling model for cascade diversion hydropower-wind-solar hybrid systems with Wasserstein-based distributionally robust chance constraints
  Renewable Energy, Vol. 254
- QoS-Aware and Routing-Flexible Network Slicing for Service-Oriented Networks
  IEEE Transactions on Network and Service Management, Vol. 22, No. 6
- Ship Scheduling and Refueling for Container Liner Cold Chain Shipping
  9 December 2025 | Mathematics, Vol. 13, No. 24
- A mixed-integer optimization formulation for buyer formation
  Computers & Operations Research, Vol. 183
- Approximation of chance constraints for surgical session scheduling using Kernel density estimation
  31 October 2025 | Flexible Services and Manufacturing Journal, Vol. 28
- A profit maximization problem of equipment rental and scheduling with split services
  15 October 2024 | IISE Transactions, Vol. 57, No. 10
- An optimisation approach for the agricultural and industrial tactical planning in the fresh fruit processing industry
  16 April 2025 | International Journal of Production Research, Vol. 63, No. 19
- Retrofitting Ordinary Portland cement production for reduced greenhouse gas emissions
  Computers & Chemical Engineering, Vol. 201
- A Reciprocity Between Tree Ensemble Optimization and Multilinear Optimization
  Jongeun Kim,
  Jean-Philippe P. Richard,
  Mohit Tawarmalani
  29 August 2024 | Operations Research, Vol. 73, No. 5
- Tight MILP formulation for pipeline gas flow with linepack
  International Journal of Electrical Power & Energy Systems, Vol. 169
- P-split formulations: a class of intermediate formulations between big-M and convex hull for disjunctive constraints
  9 June 2025 | Mathematical Programming, Vol. 75
- LinA: a faster approach to piecewise linear approximations using corridors and its application to mixed-integer optimization
  23 January 2025 | Mathematical Programming Computation, Vol. 17, No. 2
- Piecewise linear approximation using J1 compatible triangulations for efficient MILP representation
  Computers & Chemical Engineering, Vol. 196
- Bi-attribute utility preference robust optimization: A continuous piecewise linear approximation approach
  European Journal of Operational Research, Vol. 323, No. 1
- A choice-based optimization approach for service operations in multimodal mobility systems
  Transportation Research Part C: Emerging Technologies, Vol. 171
- In-orbit Servicing and Assisted Orbit Transfer Mission Planning
  30 July 2025
- Co-Optimization of Ancillary Services Providing Primary Frequency Control in the Day-Ahead Market
  IEEE Access, Vol. 13
- Efficient algorithm for addressing large-scale linear fractional program problems
  AIMS Mathematics, Vol. 10, No. <![CDATA[9]]>
- Piecewise Polyhedral Relaxations of Multilinear Optimization
  1 October 2024 | SIAM Journal on Optimization, Vol. 34, No. 4
- Optimizing peak shaving operation in hydro-dominated hybrid power systems with limited distributional information on renewable energy uncertainty
  Renewable Energy, Vol. 237
- Discretization-based solution approaches for the circle packing problem
  24 January 2024 | Engineering Optimization, Vol. 56, No. 12
- A fairness-based multi-objective distribution and restoration model for enhanced resilience of supply chain transportation networks
  Reliability Engineering & System Safety, Vol. 251
- Assessing hydropower capability for accommodating variable renewable energy considering peak shaving of multiple power grids
  Energy, Vol. 305
- Short-term load distribution model for giant cascade serial diversion-type hydropower stations
  Journal of Hydrology, Vol. 641
- A method of time-varying demand distribution estimation for high-speed railway networks with user equilibrium model
  Transportation Research Part E: Logistics and Transportation Review, Vol. 189
- Optimization methods for plastics management supply chain design
  16 May 2024 | AIChE Journal, Vol. 70, No. 8
- A ReLU-based linearization approach for maximizing oil production in subsea platforms: An application to flow splitting
  Chemical Engineering Science, Vol. 295
- RiNSES4: Rigorous Nonlinear Synthesis of Energy Systems for Seasonal Energy Supply and Storage
  9 July 2024
- Piecewise linear trees as surrogate models for system design and planning under high-frequency temporal variability
  European Journal of Operational Research, Vol. 315, No. 2
- Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part I
  30 January 2024 | Computational Optimization and Applications, Vol. 87, No. 3
- Generating hydro unit commitment instances
  11 October 2023 | TOP, Vol. 32, No. 1
- Piecewise linear approximation for MILP leveraging piecewise convexity to improve performance
  Computers & Chemical Engineering, Vol. 183
- Closed loop model predictive control of a hybrid battery-hydrogen energy storage system using mixed-integer linear programming
  Energy Conversion and Management: X, Vol. 22
- Advances in MINLP to Identify Energy-Efficient Distillation Configurations
  Radhakrishna Tumbalam Gooty,
  Rakesh Agrawal,
  Mohit Tawarmalani
  26 September 2022 | Operations Research, Vol. 72, No. 2
- Modeling combinatorial disjunctive constraints via junction trees
  26 April 2023 | Mathematical Programming, Vol. 204, No. 1-2
- Pump scheduling optimization in water distribution system based on mixed integer linear programming
  European Journal of Operational Research, Vol. 313, No. 3
- New Formulations for the Scheduled Service Network Design Problem with Piecewise Linear Costs
  28 June 2024
- Performance of Piecewise Linear Models in MILP Unit Commitment: Difference of Convex vs. J1 Approximation
- Global Optimization via Quadratic Disjunctive Programming for Water Networks Design with Energy Recovery
- A linear programming approach to difference-of-convex piecewise linear approximation
  European Journal of Operational Research, Vol. 312, No. 2
- Technicians scheduling and routing problem for elevators preventive maintenance
  Expert Systems with Applications, Vol. 235
- Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine
  Omega, Vol. 122
- Hierarchical Energy Management of Hybrid Battery Storage Systems for PV Capacity Firming and Spot Market Trading Considering Degradation Costs
  IEEE Access, Vol. 12
- An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing
  IEEE Transactions on Signal Processing, Vol. 72
- An Approximation Algorithm for Optimal Piecewise Linear Interpolations of Bounded Variable Products
  16 September 2023 | Journal of Optimization Theory and Applications, Vol. 199, No. 2
- Comparing perspective reformulations for piecewise-convex optimization
  Operations Research Letters, Vol. 51, No. 6
- Linear model decision trees as surrogates in optimization of engineering applications
  Computers & Chemical Engineering, Vol. 178
- Nonconvex Piecewise Linear Functions: Advanced Formulations and Simple Modeling Tools
  Joey Huchette,
  Juan Pablo Vielma
  31 May 2022 | Operations Research, Vol. 71, No. 5
- Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs
  5 July 2023 | Journal of Global Optimization, Vol. 87, No. 1
- Exploring the transition role of cascade hydropower in 100% decarbonized energy systems
  Energy, Vol. 279
- Optimizing bilinear multi-source water supply systems using mixed-integer linear programming approximations: An analysis of the Israeli seawater desalination array
  Advances in Water Resources, Vol. 178
- An Efficient Greedy Algorithm for Real-World Large-Scale Electric Vehicle Charging
  16 June 2023
- A reformulation technique to solve polynomial optimization problems with separable objective functions of bounded integer variables
  2 March 2023 | Optimization Letters, Vol. 17, No. 4
- On piecewise linear approximations of bilinear terms: structural comparison of univariate and bivariate mixed-integer programming formulations
  3 November 2022 | Journal of Global Optimization, Vol. 85, No. 4
- Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality
  Kevin-Martin Aigner,
  Robert Burlacu,
  Frauke Liers,
  Alexander Martin
  3 February 2023 | INFORMS Journal on Computing, Vol. 35, No. 2
- Robust Optimization for the Self-Scheduling and Bidding Strategies of a Hydroproducer Considering the Impacts of Crossing Forbidden Zones
  Journal of Water Resources Planning and Management, Vol. 149, No. 2
- Univariate Continuous Piecewise Linear Regression
  21 September 2022
- Mixed-Integer Programming Formulations for Piecewise Linear Functions
  23 September 2022
- Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions
  21 December 2022 | Journal of Optimization Theory and Applications, Vol. 196, No. 1
- Branch and price for submodular bin packing
  EURO Journal on Computational Optimization, Vol. 11
- Derivative-Free Optimization With Proxy Models for Oil Production Platforms Sharing a Subsea Gas Network
  IEEE Access, Vol. 11
- Optimizing Operations Sequencing and Demulsifier Injection in Offshore Oil Production Platforms
  IEEE Access, Vol. 11
- A Global Solution Approach to the Energy-Efficient Ladle Dispatching Problem With Refractory Temperature Control
  IEEE Access, Vol. 11
- Towards Efficient Large-Scale Network Slicing: An LP Dynamic Rounding-and-Refinement Approach
  IEEE Transactions on Signal Processing, Vol. 71
- Compact mixed-integer programming formulations in quadratic optimization
  13 June 2022 | Journal of Global Optimization, Vol. 84, No. 4
- Robust assortment optimization under sequential product unavailability
  European Journal of Operational Research, Vol. 303, No. 3
- Wasserstein metric-based two-stage distributionally robust optimization model for optimal daily peak shaving dispatch of cascade hydroplants under renewable energy uncertainties
  Energy, Vol. 260
- Identifying the critical road combination in urban roads network under multiple disruption scenarios
  Physica A: Statistical Mechanics and its Applications, Vol. 607
- Piecewise linear neural networks and deep learning
  9 June 2022 | Nature Reviews Methods Primers, Vol. 2, No. 1
- Non-convex nested Benders decomposition
  7 January 2022 | Mathematical Programming, Vol. 196, No. 1-2
- Special Issue: Global Solution of Integer, Stochastic and Nonconvex Optimization Problems
  20 August 2022 | Mathematical Programming, Vol. 196, No. 1-2
- A continuous-time formulation for optimal task scheduling and quality-of-service assurance in nanosatellites
  Computers & Operations Research, Vol. 147
- Data-driven mixed-Integer linear programming-based optimisation for efficient failure detection in large-scale distributed systems
  European Journal of Operational Research, Vol. 303, No. 1
- Partitioning approach based on convex hull and multiple choice for solving hydro unit-commitment problems
  Electric Power Systems Research, Vol. 211
- Sustainable system design of electric powertrains—comparison of optimization methods
  24 May 2021 | Engineering Optimization, Vol. 54, No. 9
- Multidisciplinary Design Optimization Approach to Integrated Space Mission Planning and Spacecraft Design
  Journal of Spacecraft and Rockets, Vol. 59, No. 5
- A Wasserstein metric-based distributionally robust optimization approach for reliable-economic equilibrium operation of hydro-wind-solar energy systems
  Renewable Energy, Vol. 196
- Ideal, non-extended formulations for disjunctive constraints admitting a network representation
  16 April 2021 | Mathematical Programming, Vol. 194, No. 1-2
- Multi-market portfolio optimization with conditional value at risk
  European Journal of Operational Research, Vol. 300, No. 1
- A mixed-integer MPC with polyhedral potential field cost for obstacle avoidance
- Advances in Mixed-Integer Model Predictive Control
- A multi-layer model of stratified thermal storage for MILP-based energy management systems
  Applied Energy, Vol. 314
- Data-Driven Generation of Mixed-Integer Linear Programming Formulations for Model Predictive Control of Hybrid Energy Storage Systems using detailed nonlinear Simulation Models
- Approach for integrated product variant allocation and configuration adaption of global production networks featuring post-optimality analysis
  1 March 2021 | International Journal of Production Research, Vol. 60, No. 7
- Short-term steady-state production optimization of offshore oil platforms: wells with dual completion (gas-lift and ESP) and flow assurance
  25 May 2021 | TOP, Vol. 30, No. 1
- Single Allocation Hub Location with Heterogeneous Economies of Scale
  Borzou Rostami,
  Masoud Chitsaz,
  Okan Arslan,
  Gilbert Laporte,
  Andrea Lodi
  28 December 2021 | Operations Research, Vol. 70, No. 2
- On refinement strategies for solving $${\textsc {MINLP}\mathrm{s}}$$ by piecewise linear relaxations: a generalized red refinement
  19 June 2021 | Optimization Letters, Vol. 16, No. 2
- The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling
  European Journal of Operational Research, Vol. 297, No. 3
- Proportionally fair flow markets for transportation networks
  Transportation Research Part B: Methodological, Vol. 157
- Shared autonomous vehicle management considering competition with human-driven private vehicles
  Transportation Research Part C: Emerging Technologies, Vol. 136
- Piecewise linear approximations for hydropower production function applied on the hydrothermal unit commitment problem
  International Journal of Electrical Power & Energy Systems, Vol. 135
- Migration-Aware Optimized Resource Allocation in B5G Edge Networks
- Piecewise Linearization of Bivariate Nonlinear Functions: Minimizing the Number of Pieces Under a Bounded Approximation Error
  21 November 2022
- Polyhedral potential field constructions for obstacle avoidance in a receding horizon formulation
  IFAC-PapersOnLine, Vol. 55, No. 16
- Exploring Symmetry in a Short-Term Hydro Scheduling Problem: The Case of the Santo Antônio Hydro Plant
  Journal of Water Resources Planning and Management, Vol. 148, No. 1
- Vessel Scheduling and Bunker Management With Speed Deviations for Liner Shipping in the Presence of Collaborative Agreements
  IEEE Access, Vol. 10
- On-Orbit Servicing Optimization Framework with High- and Low-Thrust Propulsion Tradeoff
  Journal of Spacecraft and Rockets, Vol. 59, No. 1
- New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation
  9 January 2022 | Mathematics, Vol. 10, No. 2
- Airline Network Planning: Mixed-integer non-convex optimization with demand–supply interactions
  Transportation Research Part B: Methodological, Vol. 154
- Aid Allocation for Camp‐Based and Urban Refugees with Uncertain Demand and Replenishments
  1 December 2021 | Production and Operations Management, Vol. 30, No. 12
- Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design
  Alexander J. Zolan,
  Michael S. Scioletti,
  David P. Morton,
  Alexandra M. Newman
  8 February 2021 | INFORMS Journal on Computing, Vol. 33, No. 4
- The impacts of convex piecewise linear cost formulations on AC optimal power flow
  Electric Power Systems Research, Vol. 199
- Planning approaches for stochastic capacitated lot-sizing with service level constraints
  5 June 2020 | International Journal of Production Research, Vol. 59, No. 17
- COMANDO: A Next-Generation Open-Source Framework for Energy Systems Optimization
  Computers & Chemical Engineering, Vol. 152
- Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
  Miten Mistry,
  Dimitrios Letsios,
  Gerhard Krennrich,
  Robert M. Lee,
  Ruth Misener
  18 November 2020 | INFORMS Journal on Computing, Vol. 33, No. 3
- Nonconvex multivariate piecewise-linear fitting using the difference-of-convex representation
  Computers & Chemical Engineering, Vol. 150
- Compact formulations for efficient early-phase field development optimization of multi-reservoir fields
  Computers & Chemical Engineering, Vol. 150
- Integrated flight scheduling and fleet assignment with improved supply-demand interactions
  Transportation Research Part B: Methodological, Vol. 149
- Optimization and validation of pumping system design and operation for water supply in high-rise buildings
  19 September 2020 | Optimization and Engineering, Vol. 22, No. 2
- Towards an algorithmic synthesis of thermofluid systems
  18 September 2020 | Optimization and Engineering, Vol. 22, No. 2
- Mixed integer linear programming formulations for the hydro production function in a unit-based short-term scheduling problem
  International Journal of Electrical Power & Energy Systems, Vol. 128
- Efficient Formulations and Decomposition Approaches for Power Peak Reduction in Railway Traffic via Timetabling
  Andreas Bärmann,
  Alexander Martin,
  Oskar Schneider
  23 February 2021 | Transportation Science, Vol. 55, No. 3
- Optimization problems for machine learning: A survey
  European Journal of Operational Research, Vol. 290, No. 3
- A MILP Based Framework for the Hydro Unit Commitment Considering Irregular Forbidden Zone Related Constraints
  IEEE Transactions on Power Systems, Vol. 36, No. 3
- An efficient and accurate Mixed‐integer linear programming model for long‐term operations of large‐scale hydropower systems
  23 February 2021 | IET Renewable Power Generation, Vol. 15, No. 6
- Optimistic optimization for continuous nonconvex piecewise affine functions
  Automatica, Vol. 125
- A Prime-Logarithmic Method for Optimal Reliability Design
  IEEE Transactions on Reliability, Vol. 70, No. 1
- Tuning of oil well models with production data reconciliation
  Computers & Chemical Engineering, Vol. 145
- Control Optimization of Pump Cycles in Onshore Oilfields With Network and Electric Power Constraints
  7 August 2020 | Journal of Energy Resources Technology, Vol. 143, No. 2
- Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions
  9 November 2020
- Piecewise Linear Cost Network Design
  9 December 2020
- Between Steps: Intermediate Relaxations Between Big-M and Convex Hull Formulations
  17 June 2021
- A MIP Model for Freight Consolidation in Road Transportation Considering Outsourced Fleet
  14 August 2021
- Vessel Scheduling and Refueling in Liner Shipping: Modeling Transport of Perishable Assets with a Collaborative Agreement
  11 April 2021
- Piecewise polyhedral formulations for a multilinear term
  Operations Research Letters, Vol. 49, No. 1
- Sustainable multi-commodity capacitated facility location problem with complementarity demand functions
  Transportation Research Part E: Logistics and Transportation Review, Vol. 145
- An efficient approach for the S‐shaped penalty function
  30 April 2018 | International Transactions in Operational Research, Vol. 28, No. 1
- Assortment Optimization under the Decision Forest Model
  SSRN Electronic Journal, Vol. 183
- Joint epitope selection and spacer design for string-of-beads vaccines
  29 December 2020 | Bioinformatics, Vol. 36, No. Supplement_2
- Unit-commitment via logarithmic aggregated convex combination in multi-unit hydro plants
  Electric Power Systems Research, Vol. 189
- A MILP model for hydro unit commitment with irregular vibration zones based on the constrained Delaunay triangulation method
  International Journal of Electrical Power & Energy Systems, Vol. 123
- Computational Aspects of Bayesian Solution Estimators in Stochastic Optimization
  Danial Davarnia,
  Burak Kocuk,
  Gérard Cornuéjols
  5 October 2020 | INFORMS Journal on Optimization, Vol. 2, No. 4
- Surrogate-model based MILP for the optimal design of ethylene production from shale gas
  Computers & Chemical Engineering, Vol. 141
- Multi-Objective Optimization of Gas Pipeline Networks
  2 October 2020 | Energies, Vol. 13, No. 19
- A computational performance comparison of MILP vs. MINLP formulations for oil production optimisation
  Computers & Chemical Engineering, Vol. 140
- A linearisation approach to the stochastic dynamic capacitated lotsizing problem with sequence-dependent changeovers
  6 March 2020 | International Journal of Production Research, Vol. 58, No. 16
- Optimal utilization of natural gas pipeline storage capacity under future supply uncertainty
  Computers & Chemical Engineering, Vol. 139
- On the Derivation of Continuous Piecewise Linear Approximating Functions
  Lingxun Kong,
  Christos T Maravelias
  5 May 2020 | INFORMS Journal on Computing, Vol. 32, No. 3
- Mathematical programming formulations for piecewise polynomial functions
  3 February 2020 | Journal of Global Optimization, Vol. 77, No. 3
- Data-driven maintenance and operations scheduling in power systems under decision-dependent uncertainty
  1 October 2019 | IISE Transactions, Vol. 52, No. 6
- Mixed-integer optimization methods for online scheduling in large-scale HVAC systems
  23 January 2019 | Optimization Letters, Vol. 14, No. 4
- Mixed-integer nonseparable piecewise linear models for the hydropower production function in the Unit Commitment problem
  Electric Power Systems Research, Vol. 182
- Event-Driven Network Model for Space Mission Optimization with High-Thrust and Low-Thrust Spacecraft
  Journal of Spacecraft and Rockets, Vol. 57, No. 3
- Piecewise Linear Function Fitting via Mixed-Integer Linear Programming
  Steffen Rebennack,
  Vitaliy Krasko
  23 December 2019 | INFORMS Journal on Computing, Vol. 32, No. 2
- Sourcing and Procurement Cost Allocation in Multi‐Division Firms
  1 March 2020 | Production and Operations Management, Vol. 29, No. 3
- Integrated headway and bus priority control in transit corridors with bidirectional lane segments
  Transportation Research Part C: Emerging Technologies, Vol. 111
- Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes
  14 January 2019 | Optimization Methods and Software, Vol. 35, No. 1
- Finding Global-Optimal Gearbox Designs for Battery Electric Vehicles
  15 June 2019
- Electrified Transportation Network
  23 October 2019
- Comparison of Piecewise Linearization Techniques to Model Electric Motor Efficiency Maps: A Computational Study
  25 September 2020
- Energy Arbitrage Optimization With Battery Storage: 3D-MILP for Electro-Thermal Performance and Semi-Empirical Aging Models
  IEEE Access, Vol. 8
- ReLU networks as surrogate models in mixed-integer linear programs
  Computers & Chemical Engineering, Vol. 131
- A geometric way to build strong mixed-integer programming formulations
  Operations Research Letters, Vol. 47, No. 6
- A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints
  Joey Huchette,
  Juan Pablo Vielma
  23 May 2019 | Mathematics of Operations Research, Vol. 44, No. 3
- Mixed-integer bilinear and piecewise-linear models for designing switching strategies of multilevel power converters
  Computers & Electrical Engineering, Vol. 77
- Bike network design problem with a path-size logit-based equilibrium constraint: Formulation, global optimization, and matheuristic
  Transportation Research Part E: Logistics and Transportation Review, Vol. 127
- Integer programming for urban design
  European Journal of Operational Research, Vol. 274, No. 3
- A modeling framework and local search solution methodology for a production-distribution problem with supplier selection and time-aggregated quantity discounts
  Applied Mathematical Modelling, Vol. 68
- Ellipsoidal Methods for Adaptive Choice-Based Conjoint Analysis
  18 March 2019 | Operations Research, Vol. 20
- Ellipsoidal Methods for Adaptive Choice-Based Conjoint Analysis
  Denis Sauré,
  Juan Pablo Vielma
  18 March 2019 | Operations Research, Vol. 67, No. 2
- A partial outer convexification approach to control transmission lines
  28 November 2018 | Computational Optimization and Applications, Vol. 72, No. 2
- Efficient Piecewise Linearization for a Class of Non-convex Optimization Problems: Comparative Results and Extensions
  15 February 2019
- Modeling Thermofluid Systems: An Approach Customized for Optimization
  30 August 2019
- Algorithmic System Design of Thermofluid Systems
  14 September 2018
- Three methods for robust grading
  European Journal of Operational Research, Vol. 272, No. 1
- Embedding Formulations and Complexity for Unions of Polyhedra
  Juan Pablo Vielma
  8 November 2017 | Management Science, Vol. 64, No. 10
- $$\ell _1$$-Norm Based Central Point Analysis for Asymmetric Radial Data
  29 January 2018 | Annals of Data Science, Vol. 5, No. 3
- Sequential Global Linear Programming Algorithm for Continuous Piecewise Linear Programming
- A multitree approach for global solution of ACOPF problems using piecewise outer approximations
  Computers & Chemical Engineering, Vol. 114
- Integrated Space Logistics Mission Planning and Spacecraft Design with Mixed-Integer Nonlinear Programming
  Journal of Spacecraft and Rockets, Vol. 55, No. 2
- A Holistic Concept to Design Optimal Water Supply Infrastructures for Informal Settlements Using Remote Sensing Data
  1 February 2018 | Remote Sensing, Vol. 10, No. 2
- A comparison of piecewise linear programming formulations for stochastic disassembly line balancing
  25 July 2017 | International Journal of Production Research, Vol. 55, No. 24
- Process plant layout optimization with uncertainty and considering risk
  Computers & Chemical Engineering, Vol. 106
- A piecewise McCormick relaxation-based strategy for scheduling operations in a crude oil terminal
  Computers & Chemical Engineering, Vol. 106
- Optimization of the LCD optical film cutting problem
  14 November 2016 | International Journal of Production Research, Vol. 55, No. 15
- Scheduling for a processor sharing system with linear slowdown
  20 March 2017 | Mathematical Methods of Operations Research, Vol. 86, No. 1
- Models for the piecewise linear unsplittable multicommodity flow problems
  European Journal of Operational Research, Vol. 261, No. 1
- Optimizing booster stations
  15 July 2017
- Managing RES uncertainty and stability issues in distribution systems via energy storage systems and switchable reactive power sources
- Optimization over structured subsets of positive semidefinite matrices via column generation
  Discrete Optimization, Vol. 24
- Fuzzy score technique for the optimal location of wind turbines installations
  Applied Mathematical Modelling, Vol. 44
- Integrated Methodology for Production Optimization from Multiple Offshore Reservoirs in the Santos Basin
  IEEE Transactions on Automation Science and Engineering, Vol. 14, No. 2
- Vessel scheduling in liner shipping: Modeling transport of perishable assets
  International Journal of Production Economics, Vol. 184
- Linear Reformulation of Polynomial Discrete Programming for Fast Computation
  Han-Lin Li,
  Yao-Huei Huang,
  Shu-Cherng Fang
  21 December 2016 | INFORMS Journal on Computing, Vol. 29, No. 1
- Multicriterial Design of a Hydrostatic Transmission System Via Mixed-Integer Programming
  8 March 2017
- Algorithmic System Design Using Scaling and Affinity Laws
  8 March 2017
- Optimal sizing and placement of smart-grid-enabling technologies for maximizing renewable integration
- New Multistage and Stochastic Mathematical Model for Maximizing RES Hosting Capacity—Part I: Problem Formulation
  IEEE Transactions on Sustainable Energy, Vol. 8, No. 1
- Ellipsoidal Methods for Adaptive Choice-Based Conjoint Analysis
  SSRN Electronic Journal, Vol. 20
- New multi-commodity flow formulations for the pooling problem
  2 February 2016 | Journal of Global Optimization, Vol. 66, No. 4
- An enhanced logarithmic method for signomial programming with discrete variables
  European Journal of Operational Research, Vol. 255, No. 3
- Quantifying the impact of road capacity loss on urban electrified transportation networks: An optimization based approach
  International Journal of Transportation Science and Technology, Vol. 5, No. 4
- A domain specific language for optimal pumping systems
  31 October 2016
- A multi-layer optimal chiller operation management framework
- Economic feasibility analysis and operational testing of a community energy storage system
- Computing tight bounds via piecewise linear functions through the example of circle cutting problems
  18 June 2016 | Mathematical Methods of Operations Research, Vol. 84, No. 1
- On linear conic relaxation of discrete quadratic programs
  28 January 2016 | Optimization Methods and Software, Vol. 31, No. 4
- Global optimization with spline constraints: a new branch-and-bound method based on B-splines
  3 September 2015 | Journal of Global Optimization, Vol. 65, No. 3
- Sparse signal reconstruction via concave continuous piecewise linear programming
  Digital Signal Processing, Vol. 54
- A modified hill detouring algorithm for hinging hyperplanes minimization
- Exploiting Constructive Interference for Simultaneous Wireless Information and Power Transfer in Multiuser Downlink Systems
  IEEE Journal on Selected Areas in Communications, Vol. 34, No. 5
- Identification of critical combination of vulnerable links in transportation networks – a global optimisation approach
  1 February 2016 | Transportmetrica A: Transport Science, Vol. 12, No. 4
- Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems
  30 July 2015 | Journal of Global Optimization, Vol. 64, No. 4
- Reducing Multivalued Discrete Variables in Solving Separable Task Assignment Problems
  8 July 2015 | Journal of the Operations Research Society of China, Vol. 4, No. 1
- Maximizing the U.S. Army’s Future Contribution to Global Security Using the Capability Portfolio Analysis Tool (CPAT)
  Scott J. Davis,
  Shatiel B. Edwards,
  Gerald E. Teper,
  David G. Bassett,
  Michael J. McCarthy,
  Scott C. Johnson,
  Craig R. Lawton,
  Matthew J. Hoffman,
  Liliana Shelton,
  Stephen M. Henry,
  Darryl J. Melander,
  Frank M. Muldoon,
  Brian D. Alford,
  Roy E. Rice,
  1 February 2016 | Interfaces, Vol. 46, No. 1
- Examination and Optimization of a Heating Circuit for Energy‐Efficient Buildings
  9 December 2015 | Energy Technology, Vol. 4, No. 1
- Experimental Validation of an Enhanced System Synthesis Approach
  21 February 2016
- Designing a Feedback Control System via Mixed-Integer Programming
  21 February 2016
- Global optimization of multiphase flow networks using spline surrogate models
  Computers & Chemical Engineering, Vol. 84
- Structural Investigation of Piecewise Linearized Network Flow Problems
  SIAM Journal on Optimization, Vol. 26, No. 4
- Motion- and Communication-Planning of Unmanned Aerial Vehicles in Delay Tolerant Network using Mixed-Integer Linear Programming
  Modeling, Identification and Control: A Norwegian Research Bulletin, Vol. 37, No. 2
- Scheduling pumpoff operations in onshore oilfields under electric-power constraints
  European Journal of Operational Research, Vol. 247, No. 3
- Method of hill tunneling via simplex centroid for continuous piecewise linear programming
- Finding diverse optima and near-optima to binary integer programs
  15 April 2015 | IIE Transactions, Vol. 47, No. 11
- Developing a Control Strategy for Booster Stations under Uncertain Load
  1 November 2015 | Applied Mechanics and Materials, Vol. 807
- Multicriterial Optimization of Technical Systems Considering Multiple Load and Availability Scenarios
  1 November 2015 | Applied Mechanics and Materials, Vol. 807
- A branch-cut-and-price algorithm for the piecewise linear transportation problem
  European Journal of Operational Research, Vol. 245, No. 3
- Piecewise‐linear approximations for a non‐linear transmission expansion planning problem
  1 September 2015 | IET Generation, Transmission & Distribution, Vol. 9, No. 12
- A piecewise linear-quadratic approximation for production optimization of gas-lifted oil fields
- The redesign of a warranty distribution network with recovery processes
  Transportation Research Part E: Logistics and Transportation Review, Vol. 77
- Derivative-free methods applied to daily production optimization of gas-lifted oil fields
  Computers & Chemical Engineering, Vol. 75
- Modeling of flow splitting for production optimization in offshore gas-lifted oil fields: Simulation validation and applications
  Journal of Petroleum Science and Engineering, Vol. 128
- Global optimization method for network design problem with stochastic user equilibrium
  Transportation Research Part B: Methodological, Vol. 72
- Modeling the memristor with piecewise linear function
  7 March 2014 | International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 28, No. 1
- Piecewise Linear Formulations for Downlink Wireless OFDMA Networks
  8 August 2015
- The two-dimensional vector packing problem with piecewise linear cost function
  Omega, Vol. 50
- Mixed Integer Linear Programming Formulation Techniques
  SIAM Review, Vol. 57, No. 1
- Global Optimization for Transport Network Expansion and Signal Setting
  Mathematical Problems in Engineering, Vol. 2015
- Branch-and-cut for complementarity-constrained optimization
  22 April 2014 | Mathematical Programming Computation, Vol. 6, No. 4
- Integrated Procurement Planning in Multi‐division Firms
  1 October 2014 | Production and Operations Management, Vol. 23, No. 10
- Polynomial cases of the economic lot sizing problem with cost discounts
  European Journal of Operational Research, Vol. 237, No. 2
- 2.3.2 Reducing the Effort for LCC Evaluation and Optimization
  31 October 2014 | INCOSE International Symposium, Vol. 24, No. 1
- Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems
  11 March 2014 | Journal of Global Optimization, Vol. 59, No. 2-3
- Models and solution techniques for production planning problems with increasing byproducts
  3 May 2014 | Journal of Global Optimization, Vol. 59, No. 2-3
- A MINLP approach for layout designs based on the domino hazard index
  Journal of Loss Prevention in the Process Industries, Vol. 30
- Optimization based on adaptive hinging hyperplanes and genetic algorithm
- A Mixed-Integer convex formulation for production optimization of gas-lifted oil fields with routing and pressure constraints
  Brazilian Journal of Chemical Engineering, Vol. 31, No. 2
- Resource-Constrained Assignment Problems with Shared Resource Consumption and Flexible Demand
  Chase Rainwater,
  Joseph Geunes,
  H. Edwin Romeijn
  10 October 2013 | INFORMS Journal on Computing, Vol. 26, No. 2
- A computational analysis of multidimensional piecewise-linear models with applications to oil production optimization
  European Journal of Operational Research, Vol. 232, No. 3
- Optimization and Mathematical Modeling in Computer Architecture
  25 March 2022
- Global optimization of bilinear programs with a multiparametric disaggregation technique
  3 January 2013 | Journal of Global Optimization, Vol. 57, No. 4
- Optimising production and distribution operations in large water supply networks: A piecewise linear optimisation approach
  5 November 2013 | International Journal of Production Research, Vol. 51, No. 23-24
- A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems
  Han-Lin Li,
  Yao-Huei Huang,
  Shu-Cherng Fang
  22 October 2012 | INFORMS Journal on Computing, Vol. 25, No. 4
- Locally ideal formulations for piecewise linear functions with indicator variables
  Operations Research Letters, Vol. 41, No. 6
- Incremental and encoding formulations for Mixed Integer Programming
  Operations Research Letters, Vol. 41, No. 6
- Optimizing the implementation of real-time Simulink models onto distributed automotive architectures
  Journal of Systems Architecture, Vol. 59, No. 10
- Monotonic Optimization in Communication and Networking Systems
  16 October 2013 | Foundations and Trends® in Networking, Vol. 7, No. 1
- The piecewise linear optimization polytope: new inequalities and intersection with semi-continuous constraints
  17 February 2012 | Mathematical Programming, Vol. 141, No. 1-2
- A mixed-integer linear programming model for automatic routing decisions in oil production optimization
- An improved framework for solving NLIPs with signomial terms in the objective or constraints to global optimality
  Computers & Chemical Engineering, Vol. 53
- A discretization-based approach for the optimization of the multiperiod blend scheduling problem
  Computers & Chemical Engineering, Vol. 53
- Multitask implementation of synchronous reactive models with Earliest Deadline First scheduling
- Comparison of global optimization algorithms for the design of water-using networks
  Computers & Chemical Engineering, Vol. 52
- Mixed-integer nonlinear optimization
  2 April 2013 | Acta Numerica, Vol. 22
- Branch-and-cut for separable piecewise linear optimization and intersection with semi-continuous constraints
  8 November 2012 | Mathematical Programming Computation, Vol. 5, No. 1
- Efficient model for interval goal programming with arbitrary penalty function
  19 November 2011 | Optimization Letters, Vol. 7, No. 2
- Base-2 Expansions for Linearizing Products of Functions of Discrete Variables
  Warren P. Adams,
  Stephen M. Henry,
  20 November 2012 | Operations Research, Vol. 60, No. 6
- Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations
  24 May 2012 | Mathematical Programming, Vol. 136, No. 1
- Continuous piecewise linear programming via concave optimization and genetic algorithm
- Integrated production optimization of oil fields with pressure and routing constraints: The Urucu field
  Computers & Chemical Engineering, Vol. 46
- Exact Penalty and Optimality Condition for Nonseparable Continuous Piecewise Linear Programming
  30 March 2012 | Journal of Optimization Theory and Applications, Vol. 155, No. 1
- The hill detouring method for minimizing hinging hyperplanes functions
  Computers & Operations Research, Vol. 39, No. 7
- On linear programs with linear complementarity constraints
  8 January 2011 | Journal of Global Optimization, Vol. 53, No. 1
- Fitting piecewise linear continuous functions
  European Journal of Operational Research, Vol. 219, No. 1
- Mixed integer linear programming formulations for probabilistic constraints
  Operations Research Letters, Vol. 40, No. 3
- Linear programming relaxations of a network flow problem with applications in machinery industry
- Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing
  European Journal of Operational Research, Vol. 217, No. 1
- Nonlinear system identification with continuous piecewise linear neural network
  Neurocomputing, Vol. 77, No. 1
- Using Piecewise Linear Functions for Solving MINLPs
  15 November 2011
- A Computational Analysis of Convex Combination Models for Multidimensional Piecewise-Linear Approximation in Oil Production Optimization
  IFAC Proceedings Volumes, Vol. 45, No. 8
- Parameters estimation of hinging hyperplanes using median squared error criterion
  3 August 2011 | International Journal of Control, Automation and Systems, Vol. 9, No. 4
- Modeling disjunctive constraints with a logarithmic number of binary variables and constraints
  2 July 2009 | Mathematical Programming, Vol. 128, No. 1-2
- APOGEE: Global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes
  Computers & Chemical Engineering, Vol. 35, No. 5
- The Nested Event Tree Model with Application to Combating Terrorism
  Brian J. Lunday,
  Hanif D. Sherali,
  Theodore S. Glickman,
  19 May 2010 | INFORMS Journal on Computing, Vol. 22, No. 4
- A Note on “A Superior Representation Method for Piecewise Linear Functions”
  Juan Pablo Vielma,
  Shabbir Ahmed,
  George Nemhauser,
  11 March 2010 | INFORMS Journal on Computing, Vol. 22, No. 3
- Leveraging Enterprise-Wide Purchase Volumes: Optimal Supplier Assignment in Multi-Division Firms
  SSRN Electronic Journal, Vol. 42

Volume 58, Issue 2

March-April 2010

Pages iii-514

Article Information

Supplemental Material

Metrics

Information

Received:September 01, 2008
Accepted:April 01, 2009
Published Online:October 28, 2009

Cite as

Juan Pablo Vielma, Shabbir Ahmed, George Nemhauser, (2009) Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions. Operations Research 58(2):303-315.

https://doi.org/10.1287/opre.1090.0721

Keywords

PDF download

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Mixed-Integer Models for Nonseparable Piecewise-Linear Optimization: Unifying Framework and Extensions

Supplemental Material

Volume 58, Issue 2

Article Information

Supplemental Material

Metrics

Information

Cite as

Keywords

Sign Up for INFORMS Publications Updates and News