Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints
Published Online:14 Oct 2011https://doi.org/10.1287/moor.1110.0513
References
- Integrals of set-valued functions. J. Math. Anal. Appl. (1965) 12(1):1–12Crossref, Google Scholar
- Solving stochastic mathematical programs with complementarity constraints using simulation. Math. Oper. Res. (2006) 31(4):739–760Link, Google Scholar
- An exact penalization viewpoint of constrained optimization. SIAM J. Control Optim. (1991) 29(4):968–998Crossref, Google Scholar
- Convex Analysis and Measurable Multifunctions (1977) 580(Springer-Verlag, Berlin/Heidelberg) Lecture Notes in MathematicsCrossref, Google Scholar
- Stochastic bilevel programming in structural optimization. Structual Multidisciplinary Optim. (2001) 21(5):361–371Crossref, Google Scholar
- Optimization and Nonsmooth Analysis (1983) (John Wiley & Sons, New York) Google Scholar
- The radius of metric regularity. Trans. AMS (2003) 355(2):493–517Crossref, Google Scholar
- Convex Analysis and Minimization Algorithms: II (1993) (Springer-Verlag, Berlin/Heidelberg) Crossref, Google Scholar
- On metric and calmness qualification conditions in subdifferential calculus. Set-Valued Anal. (2008) 16(2–3):199–227Crossref, Google Scholar
- Methods of Descent for Nondifferentiable Optimization (1985) 1133(Springer-Verlag, New York) Lecture Notes in MathematicsCrossref, Google Scholar
- , Lemarechal C., Mifflin R. Bundle methods in nonsmooth optimization. Nonsmooth Optimization (1978) (Pergamon Press, Oxford, UK) 79–102Google Scholar
- Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization. Math. Programming (2009) 116(1):343–368Crossref, Google Scholar
- Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints. Math. Methods Oper. Res. (2008) 67(3):423–441Crossref, Google Scholar
- Partial exact penalty for mathematical program with equilibrium constraints. Set-Valued Anal. (2008) 16(5–6):785–804Crossref, Google Scholar
- Erratum: Sensitivity analysis of the value function for optimization problems with variational inequality constraints. SIAM J. Control Optim. (2002) 41(4):1315–1319Crossref, Google Scholar
- Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
- , Migdalas A., Pardas P., Värbrand P. Piece-wise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints. Multilevel Optimization: Algorithms Complexity and Application (1998) (Kluwer Academic Publishers, Dordrecht, The Netherlands) 209–229Crossref, Google Scholar
- Exponential convergence of sample average approximation methods for a class of stochastic mathematical programs with complementarity constraints. J. Comput. Math. (2006) 24(6):733–748Google Scholar
- Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. (1993) 340(1):1–35Crossref, Google Scholar
- Generalized differential calculus for nonsmooth and set-valued mappings. J. Math. Anal. Appl. (1994) 183:250–288Crossref, Google Scholar
- Variational Analysis and Generalized Differentiation I: Basic Theory (2006) 330(Springer-Verlag, Berlin/Heidelberg) A Series of Comprehensive Studies in MathematicsCrossref, Google Scholar
- Optimality conditions for a class of mathematical programs with equilibrium constraints. Math. Oper. Res. (1999) 24(3):627–644Link, Google Scholar
- Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Constraints (1998) (Kluwer Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. (1999) 25(4):159–167Crossref, Google Scholar
- Exact penalty functions in constrained optimization. SIAM J. Optim. (1989) 27(6):1333–1360Crossref, Google Scholar
- Quantitative stability in stochastic programming: The method of probability metrics. Math. Oper. Res. (2002) 27(4):792–818Link, Google Scholar
- Analysis of sample-path optimization. Math. Oper. Res. (1996) 21(3):513–528Link, Google Scholar
- Variational Analysis (1998) (Springer-Verlag, Berlin/Heidelberg) Crossref, Google Scholar
- , Ruszczyński A., Shapiro A. Stochastic programming. Handbook in Operations Research and Management Science (2003) 10(North-Holland Publishing Company, Amsterdam) Google Scholar
- Convergence properties of a regularization sheme for mathematical programs with complementarity constraints. SIAM J. Optim. (2001) 11(4):918–936Crossref, Google Scholar
- Asymptotic analysis of stochastic programs. Ann. Oper. Res. (1991) 30(1):169–186Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints. J. Optim. Theory Appl. (2006) 128(1):223–243Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. Optim. (2008) 57(3):395–418Crossref, Google Scholar
- Capacity booking in a transportation network with stochastic demand. Proc. 20th Internat. Sympos. Math. Programming (2009) ChicagoGoogle Scholar
- Bilevel stochastic programming problems: Analysis and application to telecommunications. (2004) . Doctoral dissertation, Norwegian University of Science and Technology, Trondheim, NorwayGoogle Scholar
- Resale in vertically separated markets: Profit and consumer surplus implications. Proc. 20th Internat. Sympos. Math. Programming (2009) ChicagoGoogle Scholar
- Uniform exponential convergence of sample average random functions under general sampling with applications in stochastic programming. J. Math. Anal. Appl. (2010) 368(2):692–710Crossref, Google Scholar
- Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints. Math. Oper. Res. (2007) 32(3):648–668Link, Google Scholar
- Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints. SIAM J. Optim. (2000) 10(4):943–962Crossref, Google Scholar
- Necessary and sufficient optimality conditions for mathemtical programs with equilibrium constraints. J. Math. Anal. Appl. (2005) 307(1):305–369Crossref, Google Scholar
- Exact penalization and necessary optimality conditions for generalized bilevel programming problems. SIAM J. Optim. (1997) 7(2):481–507Crossref, Google Scholar

