Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

References

• Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.Link, Google Scholar
• Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• Ben-Tal A, Hertog DD, De Waegenaere A, Melenberg B, Rennen G (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59(2):341–357.Link, Google Scholar
• Bertsimas D, Popescu I (2002) On the relation between option and stock prices: A convex optimization approach. Oper. Res. 50(2):358–374.Link, Google Scholar
• Bertsimas D, Popescu I (2005) Optimal inequalities in probability theory: A convex optimization approach. SIAM J. Optim. 15(3):780–804.Crossref, Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, 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, Berlin).Crossref, Google Scholar
• Breton M, El Hachem S (1995) Algorithms for the solution of stochastic dynamic minimax problems. Comput. Optim. Appl. 4(4):317–345.Crossref, Google Scholar
• Chares R (2009) Cones and interior-point algorithms for structured convex optimization involving powers and exponentials. PhD thesis, École Polytechnique de Louvain, Belgium. Google Scholar
• Chen W, Sim M (2009) Goal-driven optimization. Oper. Res. 57(2):342–357.Link, Google Scholar
• Chen W, Sim M, Sun J, Teo C-P (2010) From CVaR to uncertainty set: Implications in joint chance-constrained optimization. Oper. Res. 58(2):470–485.Link, Google Scholar
• Chen X, Sim M, Sun P (2007) A robust optimization perspective on stochastic programming. Oper. Res. 55(6):1058–1071.Link, Google Scholar
• Chen X, Sim M, Sun P, Zhang J (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.Link, Google Scholar
• Chen Z, Sim M, Xiong P (2017) Adaptive robust optimization with scenario-wise ambiguity sets. Accessed November 11, 2018, http://www.optimization-online.org/DB_HTML/2017/06/6055.html.Google Scholar
• Choi M-D, Yuen Lam T, Reznick B (1995) Sums of Squares of Real Polynomials, Proceedings of Symposia in Pure Mathematics, vol. 58 (American Mathematical Society, Providence, RI), 103–126.Google Scholar
• Conn AR, Gould NIM, Toint PL (2000) Trust Region Methods (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, 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
• Dentcheva D, Ruszczyński A (2003) Optimization with stochastic dominance constraints. SIAM J. Optim. 14(2):548–566.Crossref, Google Scholar
• Dentcheva D, Ruszczyński A (2006) Portfolio optimization with stochastic dominance constraints. J. Banking Finance 30(2):433–451.Crossref, Google Scholar
• Dupačová J (1987) The minimax approach to stochastic programming and an illustrative application. Stochastics Internat. J. Probab. Stochastic Processes 20(1):73–88.Google Scholar
• El Ghaoui L, Oks M, Oustry F (2003) Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. 51(4):543–556.Link, Google Scholar
• El Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 9(1):33–52.Crossref, Google Scholar
• Esfahani PM, Kuhn D (2017) Data-driven distributionally robust optimization using the Wasserstein metric: Performance guarantees and tractable reformulations. Math. Programming 171(1-2):1–52.Google Scholar
• Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with Wasserstein distance. arXiv:1604.02199.Google Scholar
• Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2):141–153.Crossref, Google Scholar
• Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4-part-1):902–917.Link, Google Scholar
• Goh J, Sim M (2011) Robust optimization made easy with rome. Oper. Res. 59(4):973–985.Link, Google Scholar
• Grant M, Boyd S, Ye Y (2008) CVX: Matlab software for disciplined convex programming. Accessed March 11, 2019, http://cvxr.com/cvx.Google Scholar
• Grant MC, Boyd SP (2008) Graph implementations for nonsmooth convex programs. Recent Advances in Learning and Control (Springer, New York), 95–110.Crossref, Google Scholar
• Hanasusanto GA, Kuhn D, Wiesemann W (2016) A comment on “computational complexity of stochastic programming problems.” Math. Programming 159(1/2):557–569.Crossref, Google Scholar
• Hanasusanto GA, Roitch V, Kuhn D, Wiesemann W (2017) Ambiguous joint chance constraints under mean and dispersion information. Oper. Res. 65(3):751–767.Link, Google Scholar
• He S, Zhang J, Zhang S (2010) Bounding probability of small deviation: A fourth moment approach. Math. Oper. Res. 35(1):208–232.Link, Google Scholar
• Isii K (1962) On sharpness of Tchebycheff-type inequalities. Ann. Inst. Statist. Math. 14(1):185–197.Crossref, Google Scholar
• Jiang R, Guan Y (2016) Data-driven chance constrained stochastic program. Math. Programming 158(1/2):291–327.Crossref, Google Scholar
• Kaas R, Goovaerts M, Dhaene J, Denuit M (2008) Modern Actuarial Risk Theory: Using R, vol. 128 (Springer Science & Business Media, Berlin).Crossref, Google Scholar
• Lasserre JB (2001) Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3):796–817.Crossref, Google Scholar
• Lasserre J-B, Prieto-Rumeau T, Zervos M (2006) Pricing a class of exotic options via moments and SDP relaxations. Math. Finance 16(3):469–494.Crossref, Google Scholar
• MathWorks (2017) Unconstrained nonlinear optimization algorithms. Accessed January 12, 2017, https://www.mathworks.com/help/optim/ug/unconstrained-nonlinear-optimization-algorithms.html.Google Scholar
• Nemirovski A, Shapiro A (2006) Convex approximations of chance constrained programs. SIAM J. Optim. 17(4):969–996.Crossref, Google Scholar
• Nesterov Y (2000) Squared functional systems and optimization problems. High Performance Optimization (Springer, New York), 405–440.Crossref, Google Scholar
• Parrilo PA (2003) Semidefinite programming relaxations for semialgebraic problems. Math. Programming 96(2):293–320.Crossref, Google Scholar
• Pflug G, Wozabal D (2007) Ambiguity in portfolio selection. Quant. Finance 7(4):435–442.Crossref, Google Scholar
• Postek K, Ben-Tal A, den Hertog D, Melenberg B (2018) Robust optimization with ambiguous stochastic constraints under mean and dispersion information. Oper. Res. 66(3):814–833.Link, Google Scholar
• Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
• Scarf H (1958) A min-max solution of an inventory problem. Studies in the Mathematical Theory of Inventory and Production (Stanford University Press, Redwood City, CA).Google Scholar
• Shapiro A (2001) On duality theory of conic linear problems. Semi-Infinite Programming (Springer, New York), 135–165.Crossref, Google Scholar
• Shapiro A, Kleywegt A (2002) Minimax analysis of stochastic problems. Optim. Methods Software 17(3):523–542.Crossref, Google Scholar
• Sion M (1958) On general minimax theorems. Pacific J. Math. 8(1):171–176.Crossref, Google Scholar
• Skajaa A, Ye Y (2015) A homogeneous interior-point algorithm for nonsymmetric convex conic optimization. Math. Programming 150(2):391–422.Crossref, Google Scholar
• Soyster AL (1973) Technical note—convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5):1154–1157.Link, Google Scholar
• von Neumann J, Morgenstern O (1947) Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ).Google Scholar
• Wainwright JM (2015) High-Dimensional Statistics: A Non-Asymptotic Viewpoint (Cambridge University Press, Cambridge, UK).Google Scholar
• Wang Z, Glynn PW, Ye Y (2016) Likelihood robust optimization for data-driven problems. Comput. Management Sci. 13(2):241–261.Crossref, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Zhao C, Guan Y (2018) Data-driven risk-averse stochastic optimization with Wasserstein metric. Oper. Res. Lett. 46(2):262–267.Crossref, Google Scholar
• Zymler S, Kuhn D, Rustem B (2013) Distributionally robust joint chance constraints with second-order moment information. Math. Programming 137(1–2):167–198.Crossref, Google Scholar