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Asymptotical Analysis of a SAA Estimator for Optimal Value of a Two Stage Problem with Quadratic Recourse

Sainan Zhang(sainanzhzh***at***163.com)
Liwei Zhang(lwzhang***at***dlut.edu.cn)
Hongwei Zhang(hwzhang***at***dlut.edu.cn)
Qingsong Duan(qsduan***at***mail.dlut.edu.cn)

Abstract: In this paper, we first consider the stability analysis of a convex quadratic programming problem and its restricted Wolfe dual in which all parameters in the problem are perturbed. We demonstrate the upper semi-continuity of solution mappings for the primal problem and the restricted Wolfe dual problem and establish the Hadamard directionally differentiability of the optimal value function. By expressing the optimal value function as a min-max optimization problem over two compact convex sets, we present the asymptotic distribution of a SAA estimator of the optimal value for a two stage program whose second stage problem is a convex quadratic programming problem and all parameters in the quadratic program are random variables.

Keywords: quadratic programming, two stage program, stability analysis, SAA estimator, asymptotic distribution

Category 1: Stochastic Programming

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: Manuscript.

Download: [PDF]

Entry Submitted: 08/02/2016
Entry Accepted: 08/03/2016
Entry Last Modified: 08/02/2016

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