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Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems

Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems
Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems
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 explain 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.
0025-5610
1-35
Chen, Xiaojun
4255f52f-1618-47c4-9e04-69020dbce6d7
Sun, Hailin
eee2e5fb-018b-45d4-b599-08209509663c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Chen, Xiaojun
4255f52f-1618-47c4-9e04-69020dbce6d7
Sun, Hailin
eee2e5fb-018b-45d4-b599-08209509663c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Chen, Xiaojun, Sun, Hailin and Xu, Huifu (2018) Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems. Mathematical Programming, 1-35. (doi:10.1007/s10107-018-1266-4).

Record type: Article

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 explain 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.

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Submitted date: 21 June 2017
Accepted/In Press date: 24 March 2018
e-pub ahead of print date: 30 March 2018

Identifiers

Local EPrints ID: 420062
URI: http://eprints.soton.ac.uk/id/eprint/420062
ISSN: 0025-5610
PURE UUID: 556f8a9c-c900-4c15-8670-e4c1b374dfa9
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 25 Apr 2018 16:31
Last modified: 17 Dec 2019 05:32

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