Distributionally robust joint chance constraints with second-order moment information

Mathematical Programming

Volumn 137, Issue 1-2, 2013, Pages 167-198

  Zymler, Steve ^a   Kuhn, Daniel ^a   Rustem, Berç ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

90C22; Mathematics Subject Classification (2010): 90C15

Indexed keywords

BOUNDARY LAYERS; CLASSIFICATION (OF INFORMATION); CONVEX OPTIMIZATION; RESERVOIRS (WATER); VALUE ENGINEERING;

90C22; CONSTRAINT FUNCTIONS; CONVEX OPTIMIZATION ALGORITHMS; QUADRATIC CONSTRAINT FUNCTIONS; SEMI-DEFINITE PROGRAMMING; SUBJECT CLASSIFICATION; UNCERTAIN PARAMETERS; WORST CASE CONDITIONAL VALUE AT RISKS;

UNCERTAINTY ANALYSIS;

EID: 84876152184     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0494-7     Document Type: Article

References (29)

1. Alizadeh F.; Goldfarb D.: Second-order cone programming. Math. Program. 95(1), 3-51 (2003)
2. Andrieu L.; Henrion R.; Römisch W.: A model for dynamic chance constraints in hydro power reservoir management. Eur. J. Oper. Res. 207(2), 579-589 (2010)
3. Ben-Tal A.; El Ghaoui L.; Nemirovski A.: Robust Optimization. Princeton University Press, Princeton (2009)
4. Bertsimas D.; Doan X.; Natarajan K.; Teo C.P.: Models for minimax stochastic linear optimization problems with risk aversion. Math. Oper. Res. 35(3), 580-602 (2010)
5. Calafiore G.; Campi M.C.: The scenario approach to robust control design. IEEE Trans. Autom. Control 51(5), 742-753 (2006)
6. Calafiore G.; El Ghaoui L.: Distributionally robust chance-constrained linear programs with applications. J. Optim. Theory Appl. 130(1), 1-22 (2006)
7. Calafiore G.; Topcu U.; El Ghaoui L.: Parameter estimation with expected and residual-at-risk criteria. Syst. Control Lett. 58(1), 39-46 (2009)
8. Charnes A.; Cooper W.W.; Symonds G.H.: Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag. Sci. 4(3), 235-263 (1958)
9. Chen W.; Sim M.; Sun J.; Teo C.P.: From CVaR to uncertainty set: implications in joint chance-constrained optimization. Oper. Res. 58(2), 470-485 (2010)
10. Chen X.; Sim M.; Sun P.: A robust optimization perspective on stochastic programming. Oper. Res 55(6), 1058-1071 (2007)
11. Delage, E.; Ye, Y.: Distributionally robust optimization under moment uncertainty with application to data-driven problems. Oper. Res. (2010)
12. Erdoǧan E.; Iyengar G.: Ambiguous chance constrained problems and robust optimization. Math. Program. Series B 107, 37-61 (2006)
13. Goh J.; Sim M.: Robust optimization made easy with ROME. Oper. Res 59(4), 973-985 (2010)
14. Isii K.: The extrema of probability determined by generalized moments (i) bounded random variables. Ann. Inst. Stat. Math. 12(2), 119-134 (1960)
15. Kuhn D.; Wiesemann W.; Georghiou A.: Primal and dual linear decision rules in stochastic and robust optimization. Math. Program 130(1), 177-209 (2011)
16. Löfberg, J.: YALMIP: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei (2004)
17. Luedtke J.; Ahmed S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19(2), 674-699 (2008)
18. Miller L.B.; Wagner H.: Chance-constrained programming with joint constraints. Oper. Res. 13(6), 930-945 (1965)
19. Natarajan K.; Pachamanova D.; Sim M.: Constructing risk measures from uncertainty sets. Oper. Res. 57(5), 1129-1141 (2009)
20. Nemirovski A.; Shapiro A.: Convex approximations of chance constrained programs. SIAM J. Optim. 17(4), 969-996 (2006)
21. Pagnoncelli B.K.; Ahmed S.; Shapiro A.: Sample average approximation method for chance constrained programming: theory and applications. J. Optim. Theory Appl. 142(2), 399-416 (2009)
22. Pólik I.; Terlaky T.: A survey of the S-lemma. SIAM Rev. 49(3), 371-481 (2007)
23. Prékopa, A.: On probabilistic constrained programming. In: Proceedings of the Princeton Symposium on Mathematical Programming, pp. 113-138. Princeton University Press, Princeton (1970)
24. Rockafellar R.T.; Uryasev S.: Optimization of conditional value-at-risk. J. Risk 2, 21-41 (2002)
25. Shapiro A.: On duality theory of conic linear problems. In: Goberna, M.A.; Lopez, M.A. (eds) Semi-Infinite Programming: Recent Advances, Kluwer, Dordrecht (2001)
26. Shapiro A.; Kleywegt A.J.: Minimax analysis of stochastic problems. Optim. Methods Softw 17(3), 523-542 (2002)
27. Toker, O.; Ozbay, H.: On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. In: Proceedings of the American Control Conference, pp. 2525-2526. Seatle (1995)
28. Vandenberghe L.; Boyd S.; Comanor K.: Generalized Chebyshev bounds via semidefinite programming. SIAM Rev. 49, 52-64 (2007)
29. Zymler, S.; Kuhn, D.; Rustem, B.: Worst-case value-at-risk of non-linear portfolios. http://www.optimization-online.org/DB-HTML/2009/08/2379.html (2009)