Paper Info
Title
A sample average approximation regularization method for a stochastic mathematical program with general vertical complementarity constraints.
Abstract
Based on the log-exponential function, a sample average approximation (SAA) regularization method is proposed for solving a stochastic mathematical program with general vertical complementarity constraints (SMPVCC) considered by Birbil et al. (2006). Detailed convergence analysis of this method is investigated. It is demonstrated that under some regularity conditions, any accumulation point of the sequence of optimal solutions of SAA regularized problem is almost surely an optimal solution of the SMPVCC as the parameter tends to zero and the sample size tends to infinity. Furthermore, the optimal value sequence of SAA regularized problem converges to the optimal value of SMPVCC with exponential convergence rate with probability one and a sequence of stationary points of regularized SAA problem converges almost surely to a stationary point of SMPVCC. Finally, we show that a stochastic Stackelberg game can be formulated as a SMPVCC problem and an equilibrium solution can be obtained by the method proposed.
Year
DOI
Venue
2015
10.1016/j.cam.2014.11.057
J. Computational Applied Mathematics
Keywords
Field
DocType
90C30
Complementarity (molecular biology),Convergence (routing),Mathematical optimization,Mathematical analysis,Stationary point,Regularization (mathematics),Almost surely,Stackelberg competition,Limit point,Mathematics,Sample size determination
Journal
Volume
Issue
ISSN
280
C
0377-0427
Citations 
PageRank 
References 
0
0.34
3
Authors
3
Name
Order
Citations
PageRank
Jie Zhang11127.99
Ya-qi Zhang200.34
Li-Wei Zhang311.03