Optimality functions in stochastic programming

Mathematical Programming

Volumn 135, Issue 1-2, 2012, Pages 293-321

  Royset, J O ^a  

^a NAVAL POSTGRADUATE SCHOOL   (United States)

Author keywords

Algorithms; Optimality conditions; Stochastic programming; Validation analysis

Indexed keywords

CONFIDENCE INTERVAL; CONSTRAINT FUNCTIONS; EXPECTED VALUES; FUNCTION VALUES; LOCAL MINIMIZER; NONCONVEX; OPTIMAL CONTROLS; OPTIMALITY CONDITIONS; OPTIMALITY FUNCTION; QUANTITATIVE MEASURES; SAMPLE AVERAGE APPROXIMATION; SAMPLE SIZES; SEMI-INFINITE OPTIMIZATION; SOLUTION QUALITY; STATIONARITY; VALIDATION ANALYSIS;

ALGORITHMS; APPROXIMATION ALGORITHMS; STOCHASTIC PROGRAMMING;

OPTIMIZATION;

EID: 84866258660     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-011-0453-3     Document Type: Article

References (48)

1. Basova, H.G.: Reliability-based design optimization using buffered failure probability. Master's thesis, Naval Postgraduate School, Monterey, California (2010)
2. Bastin F., Cirillo C., Toint P.L.: An adaptive Monte Carlo algorithm for computing mixed logit estimators. Comput. Manage. Sci. 3(1), 55-79 (2006)
3. Bastin F., Cirillo C., Toint P.L.: Convergence theory for nonconvex stochastic programming with an application to mixed logit. Math. Program. 108(2-3), 207-234 (2006)
4. Bayraksan, G., Morton, D.P.: Assessing solution quality in stochastic programs via sampling. In: Tutorials in Operations Research, pp. 102-122. INFORMS (2009)
5. Bayraksan, G., Morton, D.P.: A sequential sampling procedure for stochastic programming. Oper. Res. (2010, to appear)
6. Bettonvil B., del Castillo E., Kleijnen J.P.C.: Statistical testing of optimality conditions in multiresponse simulation-based optimization. Eur. J. Oper. Res. 199, 448-458 (2009)
7. Billingsley P.: Probability and Measure. Wiley, New York (1995)
8. Gill, P., Murray, W., Saunders, M.: User's guide for SNOPT 5.3: A Fortran package for large-scale nonlinear programming. Technical Report SOL-98-1, System Optimization Laboratory, Stanford University, Stanford, California (1998)
9. Gürkan G., Robinson A., Robinson S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84(2), 313-333 (1999)
10. Higle J.L., Sen S.: Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming. Springer, Berlin (1996)
11. Higle J.L., Sen S.: Statistical verification of optimality conditions for stochastic programs with recourse. Ann. Oper. Res. 30, 215-240 (1991)
12. Higle J.L., Sen S.: Duality and statistical tests of optimality for two stage stochastic programs. Math. Program. 75, 257-275 (1996)
13. Holmstrom, K.: Tomlab optimization. http://tomopt.com (2009)
14. Homem-de-Mello T.: Variable-sample methods for stochastic optimization. ACM Trans. Model. Comput. Simul. 13(2), 108-133 (2003)
15. Homem-de-Mello T., Shapiro A., Spearman M.L.: Finding optimal material release times using simulation-based optimization. Manage. Sci. 45(1), 86-102 (1999)
16. Kall P., Meyer J.: Stochastic Linear Programming, Models, Theory, and Computation. Springer, Berlin (2005)
17. Kim, S.H., Nelson, B.L.: Selecting the best system. In: Simulation, pp. 501-534. Elsevier, Amsterdam (2006)
18. Kort, B.W., Bertsekas, D.P.: A New Penalty Function Algorithm for Constrained Minimization. In: Proceedings 1972 IEEE Conference on Decision and Control. New Orlean, Louisiana (1972)
19. Kushner H.J., Yin G.G.: Stochastic Approximation and Recursive Algorithms and Applications, 2 edn. Springer, Berlin (2003)
20. Luedtke J., Ahmed S.: A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19, 674-699 (2008)
21. Mak W.K., Morton D.P., Wood R.K.: Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. 24, 47-56 (1999)
22. Nemirovski A., Juditsky A., Lan G., Shapiro A.: Robust stochastic approximation approach to stochastic programming. SIAM J. Optim. 19(4), 1574-1609 (2009)
23. Nemirovski A., Shapiro A.: Convex approximations of chance constrained programs. SIAM Optim. 17(4), 969-996 (2006)
24. Norkin V.I., Pflug G.C., Ruszczynski A.: A branch and bound method for stochastic global optimization. Math. Program. 83, 425-450 (1998)
25. Pasupathy R.: On choosing parameters in retrospective-approximation algorithms for stochastic root finding and simulation optimization. Oper. Res. 58(4), 889-901 (2010)
26. Pee E.Y., Royset J.O.: On solving large-scale finite minimax problems using exponential smoothing. J. Optim. Theory Appl. 148(2), 390-421 (2011)
27. Polak E.: On the mathematical foundations of nondifferentiable optimization in engineering design. SIAM Rev. 29, 21-89 (1987)
28. Polak E.: On the use of consistent approximations in the solution of semi-infinite optimization and optimal control problems. Math. Program. Ser. B 62(1-3), 385-414 (1993)
29. Polak E.: Optimization. Algorithms and Consistent Approximations. Springer, New York (1997)
30. Polak E., Royset J.O.: Efficient sample sizes in stochastic nonlinear programming. J. Comput. Appl. Math. 217, 301-310 (2008)
31. Rao S.S.: Engineering Optimization Theory and Practice, 4th edn. Wiley, London (2009)
32. Rockafellar R.T., Royset J.O.: On buffered failure probability in design and optimization of structures. Reliabil. Eng. Syst. Safety 95, 499-510 (2010)
33. Rockafellar R.T., Uryasev S.: Conditional value-at-risk for general loss distributions. J. Bank. Finance 26, 1443-1471 (2002)
34. Royset J.O., Der Kiureghian A., Polak E.: Reliability-based optimal design of series structural systems. J. Eng. Mech. 127(6), 607-614 (2001)
35. Royset J.O., Polak E.: Extensions of stochastic optimization results from problems with simple to problems with complex failure probability functions. J. Optim. Theory Appl. 133(1), 1-18 (2007)
36. Sakalauskas L.L.: Nonlinear stochastic programming by Monte-Carlo estimators. Eur. J. Oper. Res. 137, 558-573 (2002)
37. Sakalauskas, L.L.: Towards implementable nonlinear stochastic programming. In: Coping with Uncertainty, pp. 257-279. Springer, Berlin (2006)
38. Samson, S., Thoomu, S., Fadel, G., Reneke, J.: Reliable design optimization under aleatory and epistemic uncertainty. In: Proceedings of ASME 2009 International Design Engineering Technical Conferences, pp. DETC2009-86473 (2009)
39. Shapiro A.: Asymptotic behavior of optimal solutions in stochastic programming. Math. Oper. Res. 18(4), 829-845 (1993)
40. Shapiro, A.: Testing KKT conditions. Private Communication, June 2 (2003)
41. Shapiro A., Dentcheva D., Ruszczynski A.: Lectures on Stochastic Programming: Modeling and Theory. Society of Industrial and Applied Mathematics, Philadelphia (2009)
42. Shapiro A., Homem-de-Mello T.: A simulation-based approach to two-stage stochastic programming with recourse. Math. Program. 81, 301-325 (1998)
43. Shapiro A., Xu H.: Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. J. Math. Anal. Appl. 325, 1390-1399 (2007)
44. Spall J.C.: Introduction to Stochastic Search and Optimization. Wiley, New York (2003)
45. Tong X., Qi L., Wu F., Zhou H.: A smoothing method for solving portfolio optimization with CVaR and applications in allocation of generation asset. Appl. Math. Comput. 216, 1723-1740 (2010)
46. Wallace S.W., Ziemba W.T.: Applications of Stochastic Programming. Society for Industrial and Applied Mathematics, Philadelphia (2005)
47. Wang W., Ahmed S.: Sample average approximation of expected value constrained stochastic programs. Oper. Res. Lett. 36(5), 515-519 (2008)
48. Xu H., Zhang D.: Smooth sample average approximation of stationary points in nonsmooth stochastic optimization and applications. Math. Program. 119, 371-401 (2009)