Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods
Published Online:30 Apr 2018https://doi.org/10.1287/ijoc.2017.0780
References
- (2008) MPEC problem formulations and solution strategies with chemical engineering applications. Comput. Chem. Engrg. 32(12):2903–2913.Crossref, Google Scholar
- (1989) Parallel and Distributed Computation: Numerical Methods (Prentice-Hall, Upper Saddle River, NJ).Google Scholar
- (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1):1–122.Crossref, Google Scholar
- (2011) Combination of nonlinear and linear optimization of transient gas networks. INFORMS J. Comput. 23(4):605–617.Link, Google Scholar
- (2015) Physical and technical fundamentals of gas networks. Koch T, Hiller B, Pfetsch ME, Schewe L, eds. Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization (SIAM, Philadelphia), 17–43.Crossref, Google Scholar
- (1976) A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Comput. Math. Appl. 2(1):17–40.Crossref, Google Scholar
- (2011) Towards globally optimal solutions for MINLPs by discretization techniques with applications in gas network optimization. Doctoral dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg.Google Scholar
- (2012) Using piecewise linear functions for solving MINLPs. Lee J, Leyffer S, eds. Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and Its Applications, Vol. 154 (Springer, New York), 287–314.Crossref, Google Scholar
- (2015a) The MILP-relaxation approach. Koch T, Hiller B, Pfetsch ME, Schewe L, eds. Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization (SIAM, Philadelphia), 103–122.Crossref, Google Scholar
- (2013) A new algorithm for MINLP applied to gas transport energy cost minimization. Jünger M, Reinelt G, eds. Facets of Combinatorial Optimization (Springer, Berlin), 321–353.Google Scholar
- (2015b) Solving power-constrained gas transportation problems using an MIP-based alternating direction method. Comput. Chem. Engrg. 82:303–317.Crossref, Google Scholar
- (2017) Penalty alternating direction methods for mixed-integer optimization: A new view on feasibility pumps. SIAM J. Optim. 27(3):1611–1636.Crossref, Google Scholar
- (2011) Mixed integer linear models for the optimization of dynamical transport networks. Math. Methods Oper. Res. 73(3):339–362.Crossref, Google Scholar
- (1975) Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de Dirichlet non linéaires. ESAIM: Mathematical Modelling and Numerical Analysis—Modélisation Mathématique et Analyse Numérique 9(R2):41–76.Google Scholar
- (2007) Biconvex sets and optimization with biconvex functions: A survey and extensions. Math. Methods Oper. Res. 66(3):373–407.Crossref, Google Scholar
- (2015) Gurobi optimizer reference manual. Accessed October 16, 2017, http://www.gurobi.com/documentation/7.5/refman.index.html.Google Scholar
- (1979) Exact penalty functions in nonlinear programming. Math. Programming 17(1):251–269.Crossref, Google Scholar
- , eds. (2013) Facets of Combinatorial Optimization (Springer, Berlin).Crossref, Google Scholar
- , eds. (2015) Evaluating Gas Network Capacities. SIAM-MOS Series on Optimization (SIAM) (SIAM, Philadelphia).Crossref, Google Scholar
- LaMaTTO (2016) LaMaTTO++: A framework for modeling and solving mixed-integer nonlinear programming problems on networks. Accessed October 16, 2017, http://www.mso.math.fau.de/edom/projects/lamatto.html.Google Scholar
- (2010) A mixed integer approach for time-dependent gas network optimization. Optim. Methods Software 25(4):625–644.Crossref, Google Scholar
- (2006) Mixed integer models for the stationary case of gas network optimization. Math. Programming, Ser. B 105(2):563–582.Crossref, Google Scholar
- (2009) GAMS User Guide. VERSION 23.0.Google Scholar
- (2013) Solving MINLPs on loosely-coupled networks with applications in water and gas network optimization. Doctoral dissertation, Friedrich-Alexander-Universität Erlangen-Nürnberg.Google Scholar
- (2006) Numerical Optimization, 2nd ed. Springer Series in Operations Research and Financial Engineering (Springer Verlag, Berlin).Google Scholar
- (2005) Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming (Birkhäuser, Basel, Switzerland).Crossref, Google Scholar
- (2015) Validation of nominations in gas network optimization: Models, methods, and solutions. Optimization Methods Software 30(1):15–53.Crossref, Google Scholar
- (2015) Optimization problems in natural gas transportation systems: A state-of-the-art review. Appl. Energy 147:536–555.Crossref, Google Scholar
- (2016) Computational optimization of gas compressor stations: MINLP models versus continuous reformulations. Math. Methods Oper. Res. 83(3):409–444.Crossref, Google Scholar
- (2014) BARON 14.3.1: Global Optimization of Mixed-Integer Nonlinear Programs, User’s Manual. Accessed October 16, 2017, http://www.minlp.com/downloads/docs/baron%20manual.pdf.Google Scholar
- (2015) Mathematical optimization for evaluating gas network capacities. Koch T, Hiller B, Pfetsch ME, Schewe L, eds. Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization (SIAM, Philadelphia).Google Scholar
- (2013) A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization. Doctoral dissertation, Gottfried Wilhelm Leibniz Universität, Hannover.Google Scholar
- (2013) A primal heuristic for nonsmooth mixed integer nonlinear optimization. Jünger M, Reinelt G, eds. Facets of Combinatorial Optimization (Springer, Berlin), 295–320.Crossref, Google Scholar
- (2015a) High detail stationary optimization models for gas networks. Optim. Engrg. 16(1): 131–164.Crossref, Google Scholar
- (2015b) An MPEC based heuristic. Koch T, Hiller B, Pfetsch ME, Schewe L, eds. Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization (SIAM, Philadelphia), 163–179.Crossref, Google Scholar
- (2016) High detail stationary optimization models for gas networks: Validation and results. Optim. Engrg. 17(2):437–472.Crossref, Google Scholar
- (2005) A polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2):225–249.Crossref, Google Scholar
- (2004) Math in gas and the art of linearization. Doctoral dissertation, Rijksuniversiteit Groningen.Google Scholar
- (1976) Minimization of a non-separable objective function subject to disjoint constraints. Oper. Res. 24(4): 643–657.Link, Google Scholar

