Technical Note—Two-Stage Sample Robust Optimization

References

• Beale EML (1955) On minimizing a convex function subject to linear inequalities. J. Royal Statist. Soc. 17(2):173–184.Google Scholar
• Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.Crossref, Google Scholar
• Bertsimas D, Caramanis C (2010) Finite adaptability in multistage linear optimization. IEEE Trans. Automated Control 55(12):2751–2766.Crossref, Google Scholar
• Bertsimas D, Goyal V (2012) On the power and limitations of affine policies in two-stage adaptive optimization. Math. Programming 134(2):491–531.Crossref, Google Scholar
• Bertsimas D, Shtern S, Sturt B (2018) A data-driven approach to multi-stage stochastic linear optimization. Preprint, submitted November 3, http://www.optimization-online.org/DB_FILE/2018/11/6907.pdf.Google Scholar
• Bertsimas D, Sim M, Zhang M (2019) Adaptive distributionally robust optimization. Management Sci. 65(2):604–618.Link, Google Scholar
• Birge JR, Louveaux F (2011) Introduction to Stochastic Programming (Springer Science & Business Media, New York).Crossref, Google Scholar
• Chen X, Zhang Y (2009) Uncertain linear programs: Extended affinely adjustable robust counterparts. Oper. Res. 57(6):1469–1482.Link, Google Scholar
• Chen Z, Sim M, Xiong P (2020) Robust stochastic optimization made easy with rsome. Management Sci. 66(8):3329–3339.Google Scholar
• Conforti M, Cornuejols G, Zambelli G (2014) Integer Programming (Springer, Berlin).Crossref, Google Scholar
• Dantzig GB (1955) Linear programming under uncertainty. Management Sci. 1(3-4):197–206.Link, Google Scholar
• Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):595–612.Link, Google Scholar
• Erdoğan E, Iyengar G (2006) Ambiguous chance constrained problems and robust optimization. Math. Programming 107(1-2):37–61.Crossref, Google Scholar
• Erdoğan E, Iyengar G (2007) On two-stage convex chance constrained problems. Math. Methods Oper. Res. 65(1):115–140.Crossref, Google Scholar
• Esfahani PM, Kuhn D (2018) Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1-2):115–166.Crossref, Google Scholar
• Feige U, Jain K, Mahdian M, Mirrokni V (2007) Robust combinatorial optimization with exponential scenarios. Fischetti M, Williamson DP, eds. Internat. Conf. on Integer Programming and Combinatorial Optimization (Springer, New York), 439–453.Google 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.Crossref, Google Scholar
• Güler O (2010) Foundations of Optimization, vol. 258 (Springer Science & Business Media, New York).Crossref, Google Scholar
• Hanasusanto GA, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls. Oper. Res. 66(3):849–869.Link, Google Scholar
• Hanasusanto GA, Wiesemann W (2015) K-adaptability in two-stage robust binary programming. Oper. Res. 63(4):877–891.Link, Google Scholar
• Hoffman AJ (1952) On approximate solutions of systems of linear inequalities. J. Res. National Bureau of Standards 49(4):263–265.Crossref, Google Scholar
• Jiang R, Guan Y (2018) Risk-averse two-stage stochastic program with distributional ambiguity. Oper. Res. 66(5):1390–1405.Link, Google Scholar
• King AJ, Wets RJB (1991) Epi-consistency of convex stochastic programs. Stochastics Stochastic Rep. 34(1-2):83–92.Crossref, Google Scholar
• Liu A, Liu J-G, Lu Y (2019) On the rate of convergence of empirical measure in ∞-wasserstein distance for unbounded density function. Quart. Appl. Math. 77(4):811–829.Crossref, Google Scholar
• Nemirovski A, Shapiro A (2006) Scenario approximations of chance constraints. Calafiore G, Dabbene F, eds. Probabilistic and Randomized Methods for Design Under Uncertainty (Springer, Berlin), 3–47.Crossref, Google Scholar
• Robinson SM (1996) Analysis of sample-path optimization. Math. Oper. Res. 21(3):513–528.Link, Google Scholar
• Rockafellar RT (1970) Convex Analysis (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Shapiro A (2003) Monte carlo sampling methods. Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, New York), 353–425.Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (SIAM, Philadelphia).Crossref, Google Scholar
• Trillos NG, Slepčev D (2015) On the rate of convergence of empirical measures in infinity-transportation distance. Canadian J. Math. 67(6):1358–1383.Crossref, Google Scholar
• Van Parys BPG, Esfahani PM, Kuhn D (2017) From data to decisions: Distributionally robust optimization is optimal. Preprint, submitted April 13, https://arxiv.org/abs/1704.04118.Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Xie W (2020) Tractable reformulations of two-stage distributionally robust linear programs over the type-∞ wasserstein ball. Oper. Res. Lett. 48(4):513–523.Crossref, Google Scholar
• Xu H, Caramanis C, Mannor S (2012) A distributional interpretation of robust optimization. Math. Oper. Res. 37(1):95–110.Link, Google Scholar