An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems

Joint chance-constrained optimization problems under discrete distributions arise frequently in financial management and business operations. These problems can be reformulated as mixed-integer pro...

[1]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[2]  Tom Goldstein,et al.  The Split Bregman Method for L1-Regularized Problems , 2009, SIAM J. Imaging Sci..

[3]  A. Charnes,et al.  Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil , 1958 .

[4]  Andrzej Ruszczynski,et al.  Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra , 2002, Math. Program..

[5]  René Henrion,et al.  Convexity of chance constraints with independent random variables , 2008, Comput. Optim. Appl..

[6]  Giuseppe Carlo Calafiore,et al.  Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..

[7]  Daniel Reich,et al.  A linear programming approach for linear programs with probabilistic constraints , 2013, Eur. J. Oper. Res..

[8]  Abdel Lisser,et al.  A second-order cone programming approach for linear programs with joint probabilistic constraints , 2012, Oper. Res. Lett..

[9]  Wotao Yin,et al.  Bregman Iterative Algorithms for (cid:2) 1 -Minimization with Applications to Compressed Sensing ∗ , 2008 .

[10]  George L. Nemhauser,et al.  An integer programming approach for linear programs with probabilistic constraints , 2010, Math. Program..

[11]  James R. Luedtke,et al.  Nonanticipative duality, relaxations, and formulations for chance-constrained stochastic programs , 2016, Mathematical Programming.

[12]  James R. Luedtke,et al.  A Sample Approximation Approach for Optimization with Probabilistic Constraints , 2008, SIAM J. Optim..

[13]  Myun-Seok Cheon,et al.  A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs , 2006, Math. Program..

[14]  Maria Gabriela Martinez,et al.  Regularization methods for optimization problems with probabilistic constraints , 2013, Math. Program..

[15]  George L. Nemhauser,et al.  Mixed integer linear programming formulations for probabilistic constraints , 2012, Oper. Res. Lett..

[16]  Xiaojin Zheng,et al.  Lagrangian decomposition and mixed-integer quadratic programming reformulations for probabilistically constrained quadratic programs , 2012, Eur. J. Oper. Res..

[17]  Yi Yang,et al.  Sequential Convex Approximations to Joint Chance Constrained Programs: A Monte Carlo Approach , 2011, Oper. Res..

[18]  Martin Branda,et al.  Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers , 2016, Journal of Optimization Theory and Applications.

[19]  Nilay Noyan,et al.  Mathematical programming approaches for generating p-efficient points , 2010, Eur. J. Oper. Res..

[20]  Miguel A. Lejeune,et al.  Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems , 2012, Oper. Res..

[21]  András Prékopa,et al.  ON PROBABILISTIC CONSTRAINED PROGRAMMING , 2015 .

[22]  Maria Gabriela Martinez,et al.  Augmented Lagrangian method for probabilistic optimization , 2012, Ann. Oper. Res..

[23]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[24]  B. L. Miller,et al.  Chance Constrained Programming with Joint Constraints , 1965 .

[25]  Liwei Zhang,et al.  A Smoothing Function Approach to Joint Chance-Constrained Programs , 2014, J. Optim. Theory Appl..

[26]  R. Tyrrell Rockafellar,et al.  Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging , 2019, Math. Program..

[27]  Y. Zhang,et al.  Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization , 2014, Optim. Methods Softw..

[28]  Xiaojin Zheng,et al.  Cell-and-bound algorithm for chance constrained programs with discrete distributions , 2017, Eur. J. Oper. Res..

[29]  Suvrajeet Sen Relaxations for probabilistically constrained programs with discrete random variables , 1992, Oper. Res. Lett..

[30]  Laurence A. Wolsey,et al.  Covering Linear Programming with Violations , 2014, INFORMS J. Comput..

[31]  Melvyn Sim,et al.  From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization , 2010, Oper. Res..

[32]  Bingsheng He,et al.  Linearized Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming , 2011 .

[33]  Patrizia Beraldi,et al.  A branch and bound method for stochastic integer problems under probabilistic constraints , 2002, Optim. Methods Softw..

[34]  René Henrion,et al.  On joint probabilistic constraints with Gaussian coefficient matrix , 2011, Oper. Res. Lett..

[35]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[36]  Su Zhang,et al.  A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs , 2010, Eur. J. Oper. Res..

[37]  James R. Luedtke,et al.  Chance-Constrained Binary Packing Problems , 2014, INFORMS J. Comput..

[38]  Jie Sun,et al.  An alternating direction method for solving convex nonlinear semidefinite programming problems , 2013 .

[39]  A. Nemirovski,et al.  Scenario Approximations of Chance Constraints , 2006 .

[40]  Patrizia Beraldi,et al.  The Probabilistic Set-Covering Problem , 2002, Oper. Res..

[41]  François Margot,et al.  Solving Chance-Constrained Optimization Problems with Stochastic Quadratic Inequalities , 2016, Oper. Res..

[42]  András Prékopa Sharp Bounds on Probabilities Using Linear Programming , 1990, Oper. Res..

[43]  Duan Li,et al.  On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization , 2007, SIAM J. Optim..

[44]  James R. Luedtke A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support , 2013, Mathematical Programming.