Convergence Analysis of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Equality Constraints
Published Online:1 Aug 2007https://doi.org/10.1287/moor.1070.0260
References
- A strong law of large numbers for random compact sets. Ann. Probab. (1975) 3:879–882Crossref, Google Scholar
- Consistency of minimizers and the SLLN for stochastic programs. J. Convex Anal. (1995) 2:1–17Google Scholar
- Set-Valued Analysis (1990) (Birkhauser, Boston, MA) Google Scholar
- Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis. (2004) . Working paper, Center for Economic Research, Tilburg University, Tilburg, The NetherlandsGoogle Scholar
- Introduction to Stochastic Programming (1997) (Springer-Verlag, New York) Springer Series in Operations ResearchGoogle Scholar
- On the subdifferentiability of convex functions. Proc. Amer. Math. Soc. (1965) 16:605–611Google Scholar
- Global and superlinear convergence of the smoothing Newton’s method and its application to general box constrained variational inequalities. Math. Comput. (1998) 67:519–540Crossref, Google Scholar
- Optimization and Nonsmooth Analysis (1983) (Wiley, New York) Google Scholar
- Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) (Springer, New York) Google Scholar
- A special Newton-type optimization method. Optimization (1992) 24:269–284Crossref, Google Scholar
- Estimation of derivatives of nonsmooth performance measures in regenerative systems. Math. Oper. Res. (2001) 26:741–768Link, Google Scholar
- Refinements of necessary optimality conditions in nondifferentiable programming I. Appl. Math. Optim. (1979) 5:63–82Crossref, Google Scholar
- Some noninterior continuation methods for linear complementarity problems. SIAM J. Matrix Anal. Appl. (1996) 17:851–868Crossref, Google Scholar
- Epi-consistency of convex stochastic programs. Stochastics Stochastics Rep. (1991) 34:83–92Crossref, Google Scholar
- Smoothing implicit programming approaches for stochastic mathematical programs with linear complementarity constraints. (2003) . http://www.amp.i.kyoto-u.ac.jp/tecrep/index-e.htmlGoogle Scholar
- Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
- A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints. SIAM J. Optim. (2006) 17:891–919Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints. Oper. Res. Lett. (1999) 25:159–167Crossref, Google Scholar
- Sample-path optimization of convex stochastic performance functions. Math. Programming (1996) 75:137–176Crossref, Google Scholar
- On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems. SIAM J. Control Optim. (1983) 21:179–203Crossref, Google Scholar
- Implicit smoothing and its application to optimization with piecewise smooth equality constraints. Optim. Theory Appl. (2005) 124:673–699Crossref, Google Scholar
- Analysis of sample-path optimization. Math. Oper. Res. (1996) 21:513–528Link, Google Scholar
- Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
- Stochastic convex programming: Kuhn-Tucker conditions. J. Math. Econom. (1975) 2:349–370Crossref, Google Scholar
- Variational Analysis (1998) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
- Discrete Events Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Methods (1993) (John Wiley and Sons, New York) Google Scholar
- , Ruszczyński A., Shapiro A. Stochastic programming. Handbooks in OR & MS. Stochastic Programming (2003) 10(North-Holland Publishing Company, Amsterdam, The Netherlands) Google Scholar
- A stochastic programming approach for supply chain network design under uncertainty. Eur. J. Oper. Res. (2005) 167:96–115Crossref, Google Scholar
- Introduction to piecewise smooth equations. (1994) . Habilitation thesis, University of Karlsruhe, Karlsruhe, GermanyGoogle Scholar
- , Ruszczyński A., Shapiro A. Monte Carlo sampling methods. Handbooks in OR & MS. Stochastic Programming (2003) 10(North-Holland Publishing Company, Amsterdam, The Netherlands) Crossref, Google Scholar
- Stochastic mathematical programs with equilibrium constraints. J. Optim. Theor. Appl. (2006) 128:223–243Crossref, Google Scholar
- On rate of convergence of Monte Carlo approximations of stochastic programs. SIAM J. Optim. (2000) 11:70–86Crossref, Google Scholar
- Convergence analysis of stochastic algorithms. Math. Oper. Res. (1996) 21:615–628Link, Google Scholar
- Stochastic mathematical programs with equilibrium constraints, modeling and sample average approximation. (2005) . http://www.optimization-online.org/DB_HTML/2005/01/1046.htmlGoogle Scholar
- , Nemhauser G. L., Rinnooy Kan A. H. G., Todd M. J. Stochastic programming. Handbooks in OR & MS (1989) 1(North-Holland Publishing Company, Amsterdam, The Netherlands) 573–629Google Scholar
- An MPCC approach for stochastic Stackelberg-Nash-Cournot equilibrium. Optimization (2005) 54:27–57Crossref, Google Scholar
- An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints. SIAM J. Optim. (2006) 16:670–696Crossref, Google Scholar
- Continuous approximations to generalized Jacobians. Optimization (1999) 46:221–246Crossref, Google Scholar

