Globalized Distributionally Robust Counterpart

Published Online:https://doi.org/10.1287/ijoc.2022.0274

References

  • Bayraksan G, Love D (2015) Data-driven stochastic programming using phi-divergences. The Operations Research Revolution (INFORMS), 1–19.LinkGoogle Scholar
  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.LinkGoogle Scholar
  • Ben-Tal A, Teboulle M (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.CrossrefGoogle Scholar
  • Ben-Tal A, Boyd S, Nemirovski A (2006) Extending scope of robust optimization: Comprehensive robust counterparts of uncertain problems. Math. Programming 107(1):63–89.CrossrefGoogle Scholar
  • Ben-Tal A, Brekelmans R, den Hertog D, Vial JP (2017) Globalized robust optimization for nonlinear uncertain inequalities. INFORMS J. Comput. 29(2):350–366.LinkGoogle Scholar
  • Ben-Tal A, den Hertog D, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.LinkGoogle Scholar
  • Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.LinkGoogle Scholar
  • Bertsimas D, Shtern S, Sturt B (2022) Two-stage sample robust optimization. Oper. Res. 70(1):624–640.LinkGoogle Scholar
  • Bertsimas D, Sim M, Zhang M (2019) Adaptive distributionally robust optimization. Management Sci. 65(2):604–618.LinkGoogle Scholar
  • Birge J, Louveaux F (2011) Introduction to Stochastic Programming (Springer Science & Business Media, Boston).CrossrefGoogle Scholar
  • Blanchet J, Murthy K (2019) Quantifying distributional model risk via optimal transport. Math. Oper. Res. 44(2):565–600.LinkGoogle Scholar
  • Chen Z, Kuhn D, Wiesemann W (2022) Data-driven chance constrained programs over wasserstein balls. Oper. Res.LinkGoogle Scholar
  • Chen Z, Sim M, Xiong P (2020) Robust stochastic optimization made easy with RSOME. Management Sci. 66(8):3329–3339.LinkGoogle Scholar
  • Chen Z, Sim M, Xu H (2019) Distributionally robust optimization with infinitely constrained ambiguity sets. Oper. Res. 67(5):1328–1344.LinkGoogle Scholar
  • Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.LinkGoogle Scholar
  • Dudley RM (2018) Real Analysis and Probability (CRC Press, Boca Raton, FL).Google Scholar
  • Dupačová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming. Math. Programming 95(3):493–511.CrossrefGoogle Scholar
  • El Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 9(1):33–52.CrossrefGoogle Scholar
  • Fournier N, Guillin A (2015) On the rate of convergence in Wasserstein distance of the empirical measure. Probability Theory Related Fields 162(3):707–738.CrossrefGoogle Scholar
  • Gao R, Kleywegt A (2022) Distributionally robust stochastic optimization with Wasserstein distance. Math. Oper. Res.LinkGoogle Scholar
  • Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4-part-1):902–917.LinkGoogle Scholar
  • Gotoh Jy, Kim M, Lim A (2018) Robust empirical optimization is almost the same as mean–variance optimization. Oper. Res. Lett. 46(4):448–452.CrossrefGoogle Scholar
  • Hanasusanto G, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls. Oper. Res. 66(3):849–869.LinkGoogle Scholar
  • Hanasusanto G, Roitch V, Kuhn D, Wiesemann W (2015) A distributionally robust perspective on uncertainty quantification and chance constrained programming. Math. Programming 151(1):35–62.CrossrefGoogle Scholar
  • Hu Z, Hong LJ (2013) Kullback-Leibler Divergence Constrained Distributionally Robust Optimization (Optimization Online).Google Scholar
  • Jiang R, Guan Y (2018) Risk-averse two-stage stochastic program with distributional ambiguity. Oper. Res. 66(5):1390–1405.LinkGoogle Scholar
  • Li B, Jiang R, Mathieu J (2019) Ambiguous risk constraints with moment and unimodality information. Math. Programming 173(1–2):151–192.CrossrefGoogle Scholar
  • Liu F, Chen Z, Wang S (2023) Data for “Globalized distributionally robust counterpart.” https://doi.org/10.1287/ijoc.2022.0274.cd, https://github.com/INFORMSJoC/2022.0274.Google Scholar
  • Long DZ, Sim M, Zhou M (2023) Robust satisficing. Oper. Res. 71(1):61–82.LinkGoogle Scholar
  • Mohajerin Esfahani P, Kuhn D (2018) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1–2):115–166.CrossrefGoogle Scholar
  • Pflug G, Wozabal D (2007) Ambiguity in portfolio selection. Quant. Finance 7(4):435–442.CrossrefGoogle Scholar
  • Popescu I (2005) A semidefinite programming approach to optimal-moment bounds for convex classes of distributions. Math. Oper. Res. 30(3):632–657.LinkGoogle Scholar
  • Rachev ST (1991) Probability Metrics and the Stability of Stochastic Models, vol. 269 (Wiley, New York).Google Scholar
  • Ramachandra A, Rujeerapaiboon N, Sim M (2021) Robust conic satisficing. Preprint, submitted July 14, https://arxiv.org/abs/2107.06714.Google Scholar
  • Santambrogio F (2015) Optimal Transport for Applied Mathematicians (Springer, Birkhäuser Cham).CrossrefGoogle Scholar
  • Shapiro A (2017) Distributionally robust stochastic programming. SIAM J. Optim. 27(4):2258–2275.CrossrefGoogle Scholar
  • Sim M, Tang Q, Zhou M, Zhu T (2021) The analytics of robust satisficing. Preprint, submitted April 20, https://dx.doi.org/10.2139/ssrn.3829562.Google Scholar
  • Soyster A (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.LinkGoogle Scholar
  • Tierney L (1996) Introduction to general state-space Markov chain theory. Markov Chain Monte Carlo in Practice, 59–74.Google Scholar
  • Villani C (2009) Optimal Transport: Old and New, vol. 338 (Springer, Berlin).CrossrefGoogle Scholar
  • Wang Z, Glynn PW, Ye Y (2016) Likelihood robust optimization for data-driven problems. Comput. Management Sci. 13(2):241–261.CrossrefGoogle Scholar
  • Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.LinkGoogle Scholar
  • Xie W (2019) On distributionally robust chance constrained programs with Wasserstein distance. Math. Programming. 186:1–41.Google Scholar
  • Xu H, Caramanis C, Mannor S (2012) Optimization under probabilistic envelope constraints. Oper. Res. 60(3):682–699.LinkGoogle Scholar
  • Zhao C, Guan Y (2015) Data-Driven Risk-Averse Two-Stage Stochastic Program with ζ-Structure Probability Metrics (Optimization Online).Google Scholar
  • Zolotarev VM (1976) Metric distances in spaces of random variables and their distributions. Math. USSR Sbornik 30(3):373.CrossrefGoogle Scholar
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