Distributionally robust convex optimization

Operations Research

Volumn 62, Issue 6, 2014, Pages 1358-1376

  Wiesemann, Wolfram ^a   Kuhn, Daniel ^b   Sim, Melvyn ^c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b EPFL   (Switzerland)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Ambiguous probability distributions; Conic optimization; Robust optimization

Indexed keywords

CONVEX OPTIMIZATION; DECISION MAKING;

CONFIDENCE SETS; CONIC OPTIMIZATION; DECISION MAKERS; DECISION MAKING UNDER UNCERTAINTY; PRIOR INFORMATION; ROBUST CONVEX OPTIMIZATION; ROBUST OPTIMIZATION; STATISTICAL INDICATORS;

PROBABILITY DISTRIBUTIONS;

EID: 84918535229     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.2014.1314     Document Type: Article

References (64)

1. Alizadeh F, Goldfarb D (2003) Second-order cone programming. Math. Programming 95(1):3-51.
2. Anderson D, Williams TA, Sweeney DJ (2011) Fundamentals of Business Statistics, 6th ed. (South-Western College Publishing, Mason OH).
3. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769-805.
4. Ben-Tal A, Nemirovski A (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications (SIAM, Philadelphia).
5. Ben-Tal A, Teboulle M (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3): 449-476.
6. Ben-Tal A, Bertsimas D, Brown DB (2010) A soft robust model for optimization under ambiguity. Oper. Res. 58(4):1220-1234.
7. Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, Princeton, NJ).
8. 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.
9. Bertsimas D, Brown DB (2009) Constructing uncertainty sets for robust linear optimization. Oper. Res. 57(6):1483-1495.
10. Bertsimas D, Popescu I (2004) Optimal inequalities in probability theory: A convex optimization approach. SIAM J. Optim. 15(3):780-804.
11. Bertsimas D, Sim M (2006) Tractable approximations to robust conic optimization problems. Math. Programming 107(1-2):5-36.
12. Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev. 53(3):464-501.
13. Bertsimas D, Natarajan K, Teo C-P (2006) Persistence in discrete optimization under data uncertainty. Math. Programming 108(2-3): 251-274.
14. Bertsimas D, Doan XV, Natarajan K, Teo C-P (2010) Models for minimax stochastic linear optimization problems with risk aversion. Math. Oper. Res. 35(3):580-602.
15. Birge JR, Louveaux F (1997) Introduction to Stochastic Programming, Springer Series in Operations Research (Springer, New York).
16. Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).
17. Brown DB, Sim M (2009) Satisficing measures for analysis of risky positions. Management Sci. 55(1):71-84.
18. Brown DB, De Giorgi EG, Sim M (2012) Aspirational preferences and their representation by risk measures. Management Sci. 58(11): 2095-2113.
19. Calafiore GC, El Ghaoui L (2006) On distributionally robust chance-constrained linear programs. J. Optim. Theory Appl. 130(1):1-22.
20. Casella G, Berger RL (2002) Statistical Inference, 2nd ed. (Duxbury Thomson Learning, Pacific Grove, CA).
21. Chen W, Sim M (2009) Goal driven optimization. Oper. Res. 57(2): 342-357.
22. 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.
23. Chernick MR (2007) Bootstrap Methods: A Guide for Practitioners and Researchers, 2nd ed. (Wiley-Blackwell, Chichester, UK).
24. Cheung SS, So AM-C, Wang K (2012) Linear matrix inequalities with stochastically dependent perturbations and applications to chance-constrained semidefinite optimization. SIAM J. Optim. 22(4): 1394-1430.
25. Delage E (2009) Distributionally robust optimization in context of data-driven problem. Doctoral dissertation, Stanford University, Stanford, CA.
26. Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. 58(3):596-612.
27. DeMiguel V, Nogales FJ (2009) Portfolio selection with robust estimation. Oper. Res. 57(3):560-577.
28. 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.
29. Epstein LG (1999) A definition of uncertainty aversion. Rev. Econom. Stud. 66(3):579-608.
30. Föllmer H, Schied A (2002) Convex measures of risk and trading constraints. Finance and Stochastics 6(4):429-447.
31. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W. H. Freeman, New York).
32. Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2):141-153.
33. Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902-917.
34. Gorissen BL, den Hertog D (2013) Robust counterparts of inequalities containing sums of maxima of linear functions. Eur. J. Oper. Res. 227(1):30-43.
35. Grötschel M, Lovasz L, Schrijver A (1993) Geometric Algorithms and Combinatorial Optimization, 2nd ed. (Springer, Berlin, Heidelberg).
36. Hanasusanto GA, Kuhn D, Wallace SW, Zymler S (2014) Distributionally robust multi-item newsvendor problems with multimodal demand distributions. Math. Programming, ePub ahead of print April 24, http://dx.doi.org/10.1007/s10107-014-0776-y.
37. Hu Z, Hong J (2012) Kullback-Leibler divergence constrained dis-tributionally robust optimization. Optimization Online, http://www.optimization-online.org/DB-FILE/2012/3677.pdf.
38. Isii K (1962) On sharpness of Tchebycheff-type inequalities. Ann. Inst. Statist. Math. 14(1):185-197.
39. Keynes JM (1921) A Treatise on Probability (MacMillan, London).
40. Knight FH (1921) Risk, uncertainty and profit. Hart, Schaffner and Marx, Boston.
41. Kuhn D, Wiesemann W, Georghiou A (2011) Primal and dual linear decision rules in stochastic and robust optimization. Math. Programming 130(1):177-209.
42. Lagoa CM, Barmish BR (2002) Distributionally robust Monte Carlo simulation: A tutorial survey. Basañez L, de la Puente JA, eds. Proc. 15th Internat. Federation Automatic Control World Congress, Vol. 15 (Elsevier, Amsterdam), 1-12.
43. Lam S-W, Ng TS, Sim M, Song J-H (2013) Multiple objectives satisficing under uncertainty. Oper. Res. 61(1):214-227.
44. Levi R, Perakis G, Uichanco J (2012) The data-driven newsvendor problem: New bounds and insights. Technical report, MIT Sloan School of Management, Cambridge, MA.
45. Li X, Natarajan K, Teo C-P, Zheng Z (2014) Distributionally robust mixed integer linear programs: Persistency models with applications. Eur. J. Oper. Res. 233(3):459-473.
46. Lobo M, Vandenberghe L, Boyd S, Lebret H (1998) Applications of second-order cone programming. Linear Algebra and Its Appl. 284(1-3):193-228.
47. Löfberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. IEEE Internat. Sympos. Comput. Aided Control Systems Design (IEEE, Piscataway, NJ), 284-289.
48. Michaud R (1989) The Markowitz optimization enigma: Is "optimized" optimal? Financial Analysts J. 45(1):31-42.
49. Natarajan K, Pachamanova D, Sim M (2009) Constructing risk measures from uncertainty sets. Oper. Res. 57(5):1129-1141.
50. Popescu I (2005) A semidefinite programming approach to optimalmoment bounds for convex classes of distributions. Math. Oper. Res. 30(3):632-657.
51. Prékopa A (1995) Stochastic Programming (Kluwer Academic Publishers, Dordrecht, the Netherlands).
52. Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21-41.
53. Ruszczyński A, Shapiro A, eds. ( 2003) Stochastic Programming, Handbooks in Operations Research and Management Science, Vol. 10 ( Elsevier, Amsterdam).
54. Scarf HE (1958) A min-max solution of an inventory problem. Arrow KJ, Karlin S, Scarf HE, eds. Studies in the Mathematical Theory of Inventory and Production (Stanford University Press, Stanford CA), 201-209.
55. Schrijver A (2003) Combinatorial Optimization: Polyhedra and Efficiency (Springer, Berlin).
56. Shapiro A (2001) On duality theory of conic linear problems. Semi-Infinite Programming, Chap. 7 (Kluwer Academic Publishers, Dordrecht, the Netherlands), 135-165.
57. Shapiro A, Ahmed S (2004) On a class of minimax stochastic programs. SIAM J. Optim. 14(4):1237-1249.
58. Shapiro A, Kleywegt A (2002) Minimax analysis of stochastic problems. Optim. Methods and Software 17(3):523-542.
59. Toh KC, Todd MJ, Tütüncü RH (1999) SDPT3-A matlab software package for semidefinite programming, version 1.3. Optim. Methods and Software 11(1-4):545-581.
60. Wiesemann W, Kuhn D, Rustem B (2013) Robust Markov decision processes. Math. Oper. Res. 38(1):153-183.
61. Xu H, Mannor S (2012) Distributionally robust Markov decision processes. Math. Oper. Res. 37(2):288-300.
62. Xu H, Caramanis C, Mannor S (2012) A distributional interpretation of robust optimization. Math. Oper. Res. 37(1):95-110.
63. Žáčková J (1966) On minimax solutions of stochastic linear programming problems. Časopis pro pěstování matematiky 91(4):423-430.
64. Zymler S, Kuhn D, Rustem B (2013) Distributionally robust joint chance constraints with second-order moment information. Math. Programming 137(1-2):167-198.