Optimization with Stochastic Preferences Based on a General Class of Scalarization Functions

References

• Acerbi C (2004) Coherent representations of subjective risk aversion. Szegö G, ed. Risk Measures for the 21st Century (John Wiley & Sons, Chichester, UK), 147–207.Google Scholar
• Armbruster B, Luedtke J (2015) Models and formulations for multivariate dominance constrained stochastic programs. IIE Trans. 47(1):1–14.Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J, Heath D (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
• Bellini F, Klar B, Müller A, Gianin ER (2014) Generalized quantiles as risk measures. Insurance: Math. Econom. 54:41–48.Crossref, Google Scholar
• Ben Abdelaziz F (2012) Solution approaches for the multiobjective stochastic programming. Eur. J. Oper. Res. 216(1):1–16.Crossref, Google Scholar
• Bonnans JF, Shapiro A (2000) Perturbation Analysis of Optimization Problems, Springer Series in Operations Research (Springer, New York).Crossref, Google Scholar
• Burgert C, Rüschendorf L (2006) Consistent risk measures for portfolio vectors. Insurance: Math. Econom. 38(2):289–297.Crossref, Google Scholar
• Charnes A, Cooper WW, Kortanek K (1963) Duality in semi-infinite programs and some works of Haar and Carathéodory. Management Sci. 9(2):209–228.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) Inverse stochastic dominance constraints and rank dependent expected utility theory. Math. Programming 108(2):297–311.Crossref, Google Scholar
• Dentcheva D, Ruszczyński A (2009) Optimization with multivariate stochastic dominance constraints. Math. Programming 117(1):111–127.Crossref, Google Scholar
• Dentcheva D, Wolfhagen E (2015) Optimization with multivariate stochastic dominance constraints. SIAM J. Optim. 25(1):564–588.Crossref, Google Scholar
• Doolittle EK, Muir K, Wiecek MM (2016) A note on robustness of the min-max solution to multiobjective linear programs. Internat. J. Multicriteria Decision Making 6(4):343–365.Crossref, Google Scholar
• Ehrgott M (2005) Multicriteria Optimization (Springer, Berlin).Google Scholar
• Grechuk B, Zabarankin M (2014) Inverse portfolio problem with mean-deviation model. Eur. J. Oper. Res. 234(2):481–490.Crossref, Google Scholar
• Gutjahr WJ, Pichler A (2013) Stochastic multi-objective optimization: A survey on non-scalarizing methods. Ann. Oper. Res. 236(2):475–499.Crossref, Google Scholar
• Haskell W, Xu H, Chao Q, Zhiyue Y (2016) Online risk-aware optimization. In preparation.Google Scholar
• Homem-de-Mello T, Mehrotra S (2009) A cutting surface method for uncertain linear programs with linear stochastic dominance constraints. SIAM J. Optim. 20(3):1250–1273.Crossref, Google Scholar
• Hu J, Mehrotra S (2012) Robust and stochastically weighted multiobjective optimization models and reformulations. Oper. Res. 60(4):936–953.Link, Google Scholar
• Hu J, Homem-de-Mello T, Mehrotra S (2011) Risk-adjusted budget allocation models with application in homeland security. IIE Trans. 43(12):819–839.Crossref, Google Scholar
• Hu J, Homem-de Mello T, Mehrotra S (2012) Sample average approximation of stochastic dominance constrained programs. Math. Programming 133(1–2):171–201.Crossref, Google Scholar
• Kaya C, Maurer H (2014) A numerical method for nonconvex multi-objective optimal control problems. Computational Optim. Appl. 57(3):685–702.Crossref, Google Scholar
• Küçükyavuz S, Noyan N (2016) Cut generation for optimization problems with multivariate risk constraints. Math. Programming 159(1):165–199.Crossref, Google Scholar
• Kusuoka S (2001) On law invariant coherent risk measures. Kusuoka S, Maruyama T, eds. Advances In Mathematical Economics, Vol. 3 (Springer, Tokyo), 83–95.Crossref, Google Scholar
• Liu X, Küçükyavuz S, Noyan N (2017) Robust multicriteria risk-averse stochastic programming models. Ann. Oper. Res. 259(1):259–294.Crossref, Google Scholar
• Luque M, Miettinen K, Ruiz AB, Ruiz F (2012) A two-slope achievement scalarizing function for interactive multiobjective optimization. Comput. Oper. Res. 39(7):1673–1681.Crossref, Google Scholar
• Mehrotra S, Papp D (2014) A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization. SIAM J. Optim. 24(4):1670–1697.Crossref, Google Scholar
• Miettinen K, Mäkelä MM (2002) On scalarizing functions in multiobjective optimization. OR Spectrum 24(2):193–213.Crossref, Google Scholar
• Müller A, Stoyan D (2002) Comparison Methods for Stochastic Models and Risks (John Wiley & Sons, Chichester, UK).Google Scholar
• Nikulin Y, Miettinen K, Mäkelä MM (2012) A new achievement scalarizing function based on parameterization in multiobjective optimization. OR Spectrum 34(1):69–87.Crossref, Google Scholar
• Noyan N, Rudolf G (2013) Optimization with multivariate conditional value-at-risk constraints. Oper. Res. 61(4):990–1013.Link, Google Scholar
• Noyan N, Rudolf G (2015) Kusuoka representations of coherent risk measures in general probability spaces. Ann. OR 229(1):591–605.Crossref, Google Scholar
• Noyan N, Balcik B, Atakan S (2016) A stochastic optimization model for designing last mile relief networks. Transportation Sci. 50(3):1092–1113.Link, Google Scholar
• Ogryczak W, Ruszczyński A (2002) Dual stochastic dominance and related mean-risk models. SIAM J. Optim. 13(2):60–78.Crossref, Google Scholar
• Palma CD, Nelson JD (2010) Bi-objective multi-period planning with uncertain weights: A robust optimization approach. Eur. J. Forest Res. 129(6):1081–1091.Crossref, Google Scholar
• Pflug GC, Römisch W (2007) Modelling, Managing and Measuring Risk (World Scientific Publishing, Singapore).Crossref, Google Scholar
• Rockafellar R, Uryasev S (2000) Optimization of conditional value-at-risk. J. Risk 2(3):21–41.Crossref, Google Scholar
• Rockafellar RT, Uryasev SP, Zabarankin M (2002) Deviation measures in risk analysis and optimization. Department of Industrial and Systems Engineering Working Paper (2002-7), University of Florida.Google Scholar
• Ruszczyński A, Shapiro A (2006) Optimization of risk measures. Calafiore G, Dabbene F, eds. Probabilistic and Randomized Methods for Design Under Uncertainty (Springer, London), 119–157.Crossref, Google Scholar
• Shapiro A (2013) On Kusuoka representation of law invariant risk measures. Math. Oper. Res. 38(1):142–152.Link, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory (SIAM/NPS, Philadelphia).Crossref, Google Scholar
• Steuer RE (1986) Multiple Criteria Optimization: Theory, Computation, and Application (John Wiley & Sons, New York).Google Scholar
• Wiecek MM, Ehrgott M, Engau A (2016) Continuous Multiobjective Programming (Springer New York, New York), 739–815.Crossref, Google Scholar
• Wierzbicki A (1999) Reference point approaches. Gal T, Stewart T, Hanne T, eds. Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications (Kluwer Academic Publishers, Boston), 9.1–9.39.Crossref, Google Scholar
• Willis HH, Morral AR, Kelly TK, Medby JJ (2005) Estimating terrorism risk. Technical report, The RAND Corporation, Santa Monica, CA.Google Scholar
• Yaari ME (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.Crossref, Google Scholar
• Zardari N, Ahmed K, Shirazi S, Yusop ZB (2015) Weighting Methods and Their Effects on Multi-Criteria Decision Making Model Outcomes in Water Resources Management (Springer International, Cham, Switzerland).Crossref, Google Scholar