On Deterministic Reformulations of Distributionally Robust Joint Chance Constrained Optimization Problems

A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exc...

[1]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[2]  Peter Kall,et al.  Stochastic Programming , 1995 .

[3]  Daniel Kuhn,et al.  Distributionally robust joint chance constraints with second-order moment information , 2011, Mathematical Programming.

[4]  Huan Xu,et al.  Distributionally robust chance constraints for non-linear uncertainties , 2014, Mathematical Programming.

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

[6]  Abdel Lisser,et al.  Distributionally Robust Stochastic Knapsack Problem , 2014, SIAM J. Optim..

[7]  Kristin P. Bennett,et al.  Bilinear separation of two sets inn-space , 1993, Comput. Optim. Appl..

[8]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[9]  Daniel Kuhn,et al.  Ambiguous Joint Chance Constraints Under Mean and Dispersion Information , 2017, Oper. Res..

[10]  Yanfeng Ouyang,et al.  Joint Inventory-Location Problem Under Risk of Probabilistic Facility Disruptions , 2011 .

[11]  Benjamin Pfaff,et al.  Perturbation Analysis Of Optimization Problems , 2016 .

[12]  Daniel Kuhn,et al.  Distributionally Robust Convex Optimization , 2014, Oper. Res..

[13]  Daniel Kuhn,et al.  Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations , 2015, Mathematical Programming.

[14]  R. Durrett Probability: Theory and Examples , 1993 .

[15]  Weijun Xie,et al.  Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation , 2018, IEEE Transactions on Power Systems.

[16]  Ioana Popescu,et al.  Robust Mean-Covariance Solutions for Stochastic Optimization , 2007, Oper. Res..

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

[18]  Yinyu Ye,et al.  Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems , 2010, Oper. Res..

[19]  G. Calafiore,et al.  On Distributionally Robust Chance-Constrained Linear Programs , 2006 .

[20]  Pu Li,et al.  Probabilistic analysis for optimal power flow under uncertainty , 2010 .

[21]  Alexander Shapiro,et al.  On a Class of Minimax Stochastic Programs , 2004, SIAM J. Optim..

[22]  Daniel Kuhn,et al.  A distributionally robust perspective on uncertainty quantification and chance constrained programming , 2015, Mathematical Programming.

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

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

[25]  Alexander Shapiro,et al.  Minimax analysis of stochastic problems , 2002, Optim. Methods Softw..

[26]  Ruiwei Jiang,et al.  Data-driven chance constrained stochastic program , 2015, Mathematical Programming.

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