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

Xiaojun Chen(maxjchen***at***polyu.edu.hk)
Hailin Sun(hlsun***at***njust.edu.cn)
Huifu Xu(h.xu***at***soton.ac.uk)

Abstract: 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 be solved by the well-known progressive hedging method (PHM). Moreover, we extend the discussion by considering a two-stage distributionally robust LCP (DRLCP) with moment constraints and proposing a discretization scheme for the DRLCP. As an application, we show how the SLCP and DRLCP models can be used to study equilibrium arising from two-stage duopoly game where each player plans to set up its optimal capacity at present with anticipated competition for production in future.

Keywords: Two-stage stochastic linear complementarity problem, discrete approximation, error bound, distributionally robust linear complementarity problem, ex post equilibrium

Category 1: Stochastic Programming

Category 2: Robust Optimization

Citation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong

Download: [PDF]

Entry Submitted: 06/21/2017
Entry Accepted: 06/22/2017
Entry Last Modified: 06/21/2017

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