Distributionally Robust Linear and Discrete Optimization with Marginals

References

• Agrawal S, Ding Y, Saberi A, Ye Y (2012) Price of correlations in stochastic optimization. Oper. Res. 60(1):150–162.Link, Google Scholar
• Bach F (2019) Submodular functions: From discrete to continous domains. Math. Programming 175:419–459.Crossref, Google Scholar
• Ben-Tal A, De Waegenaere B, Melenberg GR (2013) Robust solutions of optimization problems affected by uncertain probabilities. Management Sci. 59:341–357.Link, Google Scholar
• Bertsimas D, Natarajan K, Teo C-P (2004) Probabilistic combinatorial optimization: Moments, semidefinite programming and asymptotic bounds. SIAM J. Optim. 15(1):185–209.Crossref, Google Scholar
• Bertsimas D, Natarajan K, Teo C-P (2006) Persistence in discrete optimization under data uncertainty. Math. Programming, Ser. B 108(2-3):251–274.Crossref, Google Scholar
• 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.Link, Google Scholar
• Birge JR, Maddox MJ (1995) Bounds on expected project tardiness. Oper. Res. 43(5):838–850.Link, Google Scholar
• Blanchet J, Kang Y, Murthy K (2019) Robust Wasserstein profile inference and applications to machine learning. J. Appl. Probability 56(3):830–857.Crossref, Google Scholar
• Bodlaender HL, Gritzmann P, Klee V, Van Leeuwen J (1990) Computational complexity of norm-maximization. Combinatorica 10(2):203–225.Crossref, Google Scholar
• Chen X, Long DZ, Qi J (2021) Preservation of supermodularity in parametric optimization: Necessary and sufficient conditions on constraint structures. Oper. Res. 69(1):1–12.Link, Google Scholar
• Conforti M, Cornuéjols G, Zambelli G (2010) Extended formulations in combinatorial optimization. 4OR 8(1):1–48.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
• Esfahani PM, Kuhn D (2018) Data-driven distributionally robust optimization using the wasserstein metric: performance guarantees and tractable reformulations. Math. Programming 171:115–166.Crossref, Google Scholar
• Galichon A (2016) Optimal Transport Methods in Economics (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
• Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with Wasserstein distance. Preprint, submitted July 16, https://arxiv.org/abs/1604.02199.Google Scholar
• Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper. Res. 58(4):902–917.Link, Google Scholar
• Gupta D, Denton B (2008) Appointment scheduling in healthcare: Challenges and opportunities. IIE Trans. 40(9):800–819.Crossref, Google Scholar
• Haneveld WK (1986) Robustness Against Dependence in PERT: An Application of Duality and Distributions with Known Marginals (Springer, Berlin).Crossref, Google Scholar
• Khachiyan LG (1980) Polynomial algorithms in linear programming. USSR Comput. Math. Math. Phys. 20(1):53–72.Crossref, Google Scholar
• Kong Q, Lee C-Y, Teo C-P, Zheng Z (2013) Scheduling arrivals to a stochastic service delivery system using copositive cones. Oper. Res. 61(3):711–726.Link, Google Scholar
• Lai TL, Robbins H (1976) Maximally dependent random variables. Proc. National Acad. Sci. USA 73(2):286–288.Crossref, Google Scholar
• Mak HY, Rong Y, Zhang J (2015) Appointment scheduling with limited distributional information. Management Sci. 61(2):316–334.Link, Google Scholar
• Mangasarian OL, Shiau TH (1986) A variable-complexity norm maximization problem. SIAM J. Algebraic Discrete Methods 7(3):455–461.Crossref, Google Scholar
• Meilijson I (1991) Sharp bounds on the largest of some linear combinations of random variables with given marginal distributions. Probability Engrg. Inform. Sci. 5:1–14.Crossref, Google Scholar
• Meilijson I, Nadas A (1979) Convex majorization with an application to the length of critical paths. J. Appl. Probability 16(3):671–677.Crossref, Google Scholar
• Mishra VK, Natarajan K, Padmanabhan D, Teo C-P, Li X (2014) On theoretical and empirical aspects of marginal distribution choice models. Management Sci. 60(6):1511–1531.Link, Google Scholar
• Möhring RH, Schulz AS, Stork F, Uetz M (2001) On project scheduling with irregular starting time costs. Oper. Res. Lett. 28:149–154.Crossref, Google Scholar
• Murota K (2003) Discrete Convex Analysis: Monographs on Discrete Mathematics and Applications 10 (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
• Nadas A (1979) Probabilistic PERT. IBM J. Res. Development 23(3):339–347.Crossref, Google Scholar
• Natarajan K, Song M, Teo C-P (2009) Persistency model and its applications in choice modeling. Management Sci. 55(3):453–469.Link, Google Scholar
• Pass B (2015) Multi-marginal optimal transport: Theory and applications. ESAIM Math. Model. Numerical Anal. 49:1771–1790.Crossref, Google Scholar
• Queyranne M, Tardella F (2006) Bimonotone linear inequalities and sublattices of Rn. Linear Algebra Appl. 413(1):100–120.Crossref, Google Scholar
• Rachev ST, Rüschendorf L (1998). Mass Transportation Problems: Volume I: Theory (Springer, Berlin).Google Scholar
• Rockafellar RT (1997) Convex Analysis (Princeton University Press, Princeton, NJ).Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2014) Lectures on Stochastic Programming: Modeling and Theory, 2nd ed. (SIAM, Philadelphia).Crossref, Google Scholar
• Shioura A, Tamura A (2015) Gross substitutes condition and discrete concavity for multi-unit valuations: a survey. J. Oper. Res. Soc. Japan 58(1):61–103.Crossref, Google Scholar
• Van Parys BPG, Goulart PJ, Embrechts P (2016) Fréchet inequalities via convex optimization. Optim. Online 1–22.Google Scholar
• Veinott AF Jr (1989) Representation of general and polyhedral subsemilattices and sublattices of product spaces. Linear Algebra Appl. 114:681–704.Crossref, Google Scholar
• Villani C (2003) Topics in Optimal Transportation (American Mathematical Society, Providence, RI).Crossref, Google Scholar
• Villani C (2009) Optimal Transport: Old and New. Fundamental Principles of Mathematical Sciences (Springer-Verlag, Berlin).Crossref, Google Scholar
• Weiss G (1986) Stochastic bounds on distributions of optimal value functions with applications to PERT, network flows and reliability. Oper. Res. 34(4):595–605.Link, Google Scholar
• Wiesemann W, Kuhn D, Sim M (2014) Distributionally robust convex optimization. Oper. Res. 62(6):1358–1376.Link, Google Scholar
• Zangwill WI (1966) A deterministic multi-period production scheduling model with backlogging. Management Sci. 13(1):105–119.Link, Google Scholar
• Zangwill WI (1969) A backlogging model and a multi-echelon model of a dynamic economic lot size production system: A network approach. Management Sci. 15(9):506–527.Link, Google Scholar