Discrete Nonlinear Optimization by State-Space Decompositions
Published Online:29 Nov 2017https://doi.org/10.1287/mnsc.2017.2849
References
- (2009) Constraint integer programming: Techniques and applications. ZIB-Report 08-43, Zuse Institute Berlin, Berlin.Google Scholar
- (2008) Relaxations of weakly coupled stochastic dynamic programs. Oper. Res. 56(3):712–727.Link, Google Scholar
- (1993) Network Flows: Theory, Algorithms, and Applications (Prentice Hall, Upper Saddle River, NJ).Google Scholar
- (2007) A constraint store based on multivalued decision diagrams. Bessiere C, ed. Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 4741 (Springer, Berlin), 118–132.Crossref, Google Scholar
- (2008) Polymatroids and mean-risk minimization in discrete optimization. Oper. Res. Lett. 36(5):618–622.Crossref, Google Scholar
- (2012) On the prevention of fraud and privacy exposure in process information flow. INFORMS J. Comput. 24(3):416–432.Link, Google Scholar
- (2014) A decision methodology for managing operational efficiency and information disclosure risk in healthcare processes. Decision Support Systems 57(January):406–416.Crossref, Google Scholar
- (2012) New state-space relaxations for solving the traveling salesman problem with time windows. INFORMS J. Comput. 24(3):356–371.Link, Google Scholar
- (2012) Portfolio-optimization models for small investors. Math. Methods Oper. Res. 77(3):345–356.Crossref, Google Scholar
- (2012) Mean-variance-skewness-kurtosis portfolio optimization with return and liquidity. Comm. Math. Finance 1(1):13–49.Google Scholar
- (2011) Manipulating MDD relaxations for combinatorial optimization. Achterberg T, Beck JC, eds. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Lecture Notes in Computer Science, Vol. 6697 (Springer, Berlin), 20–35.Crossref, Google Scholar
- (2014) Optimization bounds from binary decision diagrams. INFORMS J. Comput. 26(2):253–268.Link, Google Scholar
- (2016) Discrete optimization with decision diagrams. INFORMS J. Comput. 28(1):47–66.Link, Google Scholar
- (1999) Nonlinear Programming (Athena Scientific, Belmont, MA).Google Scholar
- (2012) Dynamic Programming and Optimal Control, 4th ed. (Athena Scientific, Belmont, MA).Google Scholar
- (2005) An algorithm for portfolio optimization with transaction costs. Management Sci. 51(11):1676–1688.Link, Google Scholar
- (1997) Introduction to Stochastic Programming (Springer, Berlin).Google Scholar
- (2004) Convex Optimization (Cambridge University Press, New York).Crossref, Google Scholar
- (1986) Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. C-35(8):677–691.Crossref, Google Scholar
- (1994) Exact and ordinary lumpability in finite Markov chains. J. Appl. Probab. 31(1):59–75.Crossref, Google Scholar
- (2016) Optimizing the deployment of public access defibrillators. Management Sci. 62(12):3617–3635.Link, Google Scholar
- (1981) State-space relaxation procedures for the computation of bounds to routing problems. Networks 11(2):145–164.Crossref, Google Scholar
- (2013) Multivalued decision diagrams for sequencing problems. Oper. Res. 61(6):1411–1428.Link, Google Scholar
- COIN-OR (2016) IPOPT 3.11.8. Accessed January 10, https://projects.coin-or.org/Ipopt.Google Scholar
- (2010) Extended formulations in combinatorial optimization. 4OR 8(1):1–48.Crossref, Google Scholar
- (1998) Combinatorial Optimization (John Wiley & Sons, New York).Google Scholar
- (2014) Assortment optimization under variants of the nested logit model. Oper. Res. 62(2):250–273.Link, Google Scholar
- (2007) AND/OR search spaces for graphical models. Artificial Intelligence 171(2):73–106.Crossref, Google Scholar
- (1970) Finite State Markovian Decision Processes (Academic Press, Orlando, FL).Google Scholar
- (2015) Robustness to dependency in portfolio optimization using overlapping marginals. Oper. Res. 63(6):1468–1488.Link, Google Scholar
- (2005) Advanced BDD Optimization, 1st ed. (Springer, Dordrecht, Netherlands).Google Scholar
- (1987) Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. 35(6): 832–848.Link, Google Scholar
- (2016) Near-optimal algorithms for the assortment planning problem under dynamic substitution and stochastic demand. Oper. Res. 64(1):219–235.Link, Google Scholar
- (2008) Fundamentals of Queueing Theory, 4th ed. (Wiley-Interscience, New York).Crossref, Google Scholar
- (2008) On automata, MDDs and BDDs in constraint satisfaction. Proc. ECAI 2008 Workshop Inference Methods Based Graphical Structures Knowledge (European Association for Artificial Intelligence, Bruxelles, Belgium).Google Scholar
- (2010) Portfolio selection with higher moments. Quant. Finance 10(5):469–485.Crossref, Google Scholar
- (2010) A systematic approach to MDD-based constraint programming. Cohen D, ed. Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, Vol. 6308 (Springer, Berlin), 266–280.Crossref, Google Scholar
- (2013) Decision diagrams and dynamic programming. Gomes C, Sellmann M, eds. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems—Proc. CPAIOR 2013, Lecture Notes in Computer Science, Vol. 7874 (Springer, Berlin), 94–110.Crossref, Google Scholar
- Intel (2015) Intel Math Kernel Library. Accessed December 5, https://software.intel.com/en-us/intel-mkl.Google Scholar
- (2016) A cycle-based formulation and valid inequalities for DC power transmission problems with switching. Oper. Res. 64(4):922–938.Link, Google Scholar
- (2014) Submodular function maximization. Bordeaux L, Hamadi Y, Kohli P, eds. Tractability: Practical Approaches to Hard Problems (Cambridge University Press, Cambridge, UK), 71–104.Crossref, Google Scholar
- (2011) Modeling and optimization of risk. Surveys Oper. Res. Management Sci. 16(2):49–66.Crossref, Google Scholar
- (2015) The d-level nested logit model: Assortment and price optimization problems. Oper. Res. 63(2):325–342.Link, Google Scholar
- (2007) Portfolio optimization with linear and fixed transaction costs. Ann. Oper. Res. 152(1):341–365.Crossref, Google Scholar
- (1990) Polyhedral characterization of discrete dynamic programming. Oper. Res. 38(1):127–138.Link, Google Scholar
- (2014) A branch-and-cut algorithm for the latent-class logit assortment problem. Discrete Appl. Math. 164(Part 1):246–263.Crossref, Google Scholar
- (1999) Automata and binary decision diagrams. Champarnaud JM, Ziadi D, Maurel D, eds. Automata Implementation—WIA 1998, Lecture Notes in Computer Science, Vol. 1660 (Springer, Berlin), 178–182.Crossref, Google Scholar
- (2002) State space relaxation and search strategies in dynamic programming. Koenig S, Holte RC, eds. Abstraction, Reformulation, and Approximation—SARA 2002, Lecture Notes in Computer Science, Vol. 2371 (Springer, Berlin), 51–51.Crossref, Google Scholar
- (2009) A column generation algorithm for choice-based network revenue management. Oper. Res. 57(3):769–784.Link, Google Scholar
- (2005) A comparison of complete global optimization solvers. Math. Programming 103(2):335–356.Crossref, Google Scholar
- (2005) Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming, International Series of Numerical Mathematics, Vol. 152 (Birkh/”auser, Basel, Switzerland).Google Scholar
- (2013) Optimization with multivariate conditional value-at-risk constraints. Oper. Res. 61(4):990–1013.Link, Google Scholar
- Pardalos PM, Pitsoulis LS, eds. (2000) Nonlinear Assignment Problems: Algorithms and Applications (Kluwer Academic Publishers, Dordrecht, Netherlands).Crossref, Google Scholar
- (2002) State aggregation in Markov decision processes. Proc. 41st IEEE Conf. Decision and Control, Vol. 4 (IEEE, Piscataway, NJ), 3819–3824.Google Scholar
- (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
- (2016) BARON User Manual 16.8.24: Global Optimization of Mixed-Integer Nonlinear Programs (Optimization Firm, Urbana, IL). http://www.minlp.com/downloads/docs/baron%20manual.pdf.Google Scholar
- (2013) Abstraction in Artificial Intelligence and Complex Systems (Springer, New York).Crossref, Google Scholar
- (2014) Portfolio selection and optimization with higher moments: Evidence from the Indian stock market. Asia-Pacific Financial Markets 21(2):133–149.Crossref, Google Scholar
- (2005) Trade-offs between customer service and cost in integrated supply chain design. Manufacturing Service Oper. Management 7(3):188–207.Link, Google Scholar
- (2002) Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming—Theory, Algorithms, Software, and Applications, Vol. 65, 1st ed. (Springer, Dordrecht, Netherlands).Google Scholar
- (2003) Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Math. Programming 99(3):563–591.Crossref, Google Scholar
- (2005) A polyhedral branch-and-cut approach to global optimization. Math. Programming 103(2):225–249.Crossref, Google Scholar
- (2018) SCIP: Global optimization of mixed-integer nonlinear programs in a branch-and-cut framework. Optim. Methods Software 33(3):563–593.Crossref, Google Scholar
- (2015) Service supply chain management: A review of operational models. Eur. J. Oper. Res. 247(3):685–698.Crossref, Google Scholar
- Zuse Institute Berlin (2015) SCIP 3.2.1. Accessed December 1, http://scip.zib.de/.Google Scholar

