# A Regularized Sample Average Approximation Method for Stochastic Mathematical Programs with Nonsmooth Equality Constraints

@article{Meng2006ARS, title={A Regularized Sample Average Approximation Method for Stochastic Mathematical Programs with Nonsmooth Equality Constraints}, author={Fanwen Meng and Huifu Xu}, journal={SIAM J. Optim.}, year={2006}, volume={17}, pages={891-919} }

We investigate a class of two stage stochastic programs where the second stage problem is subject to nonsmooth equality constraints parameterized by the first stage variant and a random vector. We consider the case when the parametric equality constraints have more than one solution. A regularization method is proposed to deal with the multiple solution problem, and a sample average approximation method is proposed to solve the regularized problem. We then investigate the convergence of…

## 29 Citations

### Convergence Analysis of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Equality Constraints

- Mathematics, Computer ScienceMath. Oper. Res.
- 2007

A uniform Strong Law of Large Numbers for random compact set-valued mappings is derived and used to investigate the convergence of Karush-Kuhn-Tucker points of SAA programs as the sample size increases.

### Stability Analysis of Two-Stage Stochastic Mathematical Programs with Complementarity Constraints via NLP Regularization

- Mathematics, Computer ScienceSIAM J. Optim.
- 2011

A detailed stability analysis is carried out of the approximated problems, including continuity and local Lipschitz continuity of optimal value functions and outer semicontinuity and continuity of the set of optimal solutions and stationary points.

### Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints

- MathematicsMath. Oper. Res.
- 2011

It is shown under some moderate conditions that the statistical estimators obtained from solving the penalized SAA problems converge almost surely to its true counterpart as the sample size increases.

### A sample average approximation method based on a D-gap function for stochastic variational inequality problems

- Mathematics
- 2013

Sample average approximation method is one of the well-behaved methods in the stochastic optimization.
This paper presents a sample average approximation method based on a D-gap function for…

### Sample average approximation method for a class of stochastic variational inequality problems

- MathematicsJ. Syst. Sci. Complex.
- 2011

The authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems and investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems.

### A smooth penalty-based sample average approximation method for stochastic complementarity problems

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2015

### Smooth sample average approximation of stationary points in nonsmooth stochastic optimization and applications

- MathematicsMath. Program.
- 2009

A smoothing scheme for a general class of nonsmooth stochastic problems is considered and the convergence of stationary points of the smoothed sample average approximation problem as sample size increases is investigated and an error bound on approximate stationary points is obtained.

### Quantitative stability of two-stage stochastic linear variational inequality problems with fixed recourse

- MathematicsApplicable Analysis
- 2020

ABSTRACT This paper focus on the quantitative stability of a class of two-stage stochastic linear variational inequality problems whose second stage problems are stochastic linear complementarity…

### Entropic Approximation for Mathematical Programs with Robust Equilibrium Constraints

- MathematicsSIAM J. Optim.
- 2014

By relaxing the complementarity constraints and then randomizing the index set of SICC, the well-known entropic risk measure is employed to approximate the semi-infinite constraints with a finite number of stochastic inequality constraints.

### Convergence of Stationary Points of Sample Average Two-Stage Stochastic Programs: A Generalized Equation Approach

- Mathematics, Computer ScienceMath. Oper. Res.
- 2011

It is shown under moderate conditions that an accumulation point of the SAA stationary points satisfies a relaxed stationary condition for the true problem and further that, with probability approaching one exponentially fast with increasing sample size, a stationary point of SAA converges to the set of relaxed stationary points.

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