Jie Zhang – Optimization Online

Quantitative Stability Analysis for Distributionally Robust Optimization With Moment Constraints

Published: 2015/09/17

Robust Optimization, Stochastic Programming distributionally robust optimization, holder continuity of the optimal value function, moment conditions with cone constraints, outer semicontinuity of the set of optimal solutions, quantitative stability analysis

In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is dened through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment … Read more

Quantitative Stability Analysis of Stochastic Quasi-Variational Inequality Problems and Applications

Published: 2015/06/03

Huifu Xu

Liwei Zhang

Jie Zhang

Stochastic Programming mathematical program with sqvip constraints, mathematical program with stochastic semidenite constraints, quantitative stability analysis, stochastic quasi-variational inequality

We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is dened over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation … Read more