Yongchao Liu – Optimization Online

Quantitative Stability Analysis of Stochastic Generalized Equations

Published: 2012/06/11, Updated: 2013/07/14

Stochastic Programming dominance constraints, equicontinuity, equilibrium constraints, stability analysis, stationary points, stochastic generalized equations, stochastic programs, two stage

We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem and a stochastic equilibrium problem. We derive quantitative continuity of expected value of the set-valued mapping with … Read more

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

Published: 2010/03/21

Gui-Hua Lin

Yongchao Liu

Huifu Xu

Complementarity and Variational Inequalities, Stochastic Programming mpec-mfcq, nlp-regularization, sample average approximation, smpcc, stability analysis

This paper presents numerical approximation schemes for a two stage stochastic programming problem where the second stage problem has a general nonlinear complementarity constraint: first, the complementarity constraint is approximated by a parameterized system of inequalities with a well-known regularization approach (SIOPT, Vol.11, 918-936) in deterministic mathematical programs with equilibrium constraints; the distribution of the … Read more