discrete approximation – Optimization Online

Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems

Published: 2018/12/08, Updated: 2018/12/11

Robust Optimization, Stochastic Programming decomposition, discrete approximation, distributionally robust optimization, kantorovich ball, moment conditions, parallel computing

Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … Read more

Discrete Approximation of Two-Stage Stochastic and Distributionally Robust Linear Complementarity Problems

Published: 2017/06/21

Xiaojun Chen

Hailin Sun

Huifu Xu

Robust Optimization, Stochastic Programming discrete approximation, distributionally robust optimization, error bound, ex post equilibrium, two-stage stochastic linear complementarity problem

In this paper, we propose a discretization scheme for the two-stage stochastic linear complementarity problem (LCP) where the underlying random data are continuously distributed. Under some moderate conditions, we derive qualitative and quantitative convergence for the solutions obtained from solving the discretized two-stage stochastic LCP (SLCP). We ex- plain how the discretized two-stage SLCP may … Read more