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An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints

An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints
An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints
In this paper, we consider a class of stochastic mathematical programs in which the complementarity constraints are subject to random factors and the objective function is the mathematical expectation of a smooth function which depends on both upper and lower level variables and random factors. We investigate the existence, uniqueness, and differentiability of the lower level equilibrium defined by the complementarity constraints %and its dependence using a nonsmooth version of implicit function theorem. We also study the differentiability and convexity of the objective function which implicitly depends upon the lower level equilibrium. We propose numerical methods to deal with difficulties due to the continuous distribution of the random variables and intrinsic nonsmoothness of lower level equilibrium solutions due to the complementarity constraints in order that the treated programs can be readily solved by available numerical methods for deterministic mathematical programs with complementarity constraints.
1052-6234
670-696
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Xu, Huifu (2006) An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints. SIAM Journal on Optimization, 16 (3), 670-696. (doi:10.1137/040608544).

Record type: Article

Abstract

In this paper, we consider a class of stochastic mathematical programs in which the complementarity constraints are subject to random factors and the objective function is the mathematical expectation of a smooth function which depends on both upper and lower level variables and random factors. We investigate the existence, uniqueness, and differentiability of the lower level equilibrium defined by the complementarity constraints %and its dependence using a nonsmooth version of implicit function theorem. We also study the differentiability and convexity of the objective function which implicitly depends upon the lower level equilibrium. We propose numerical methods to deal with difficulties due to the continuous distribution of the random variables and intrinsic nonsmoothness of lower level equilibrium solutions due to the complementarity constraints in order that the treated programs can be readily solved by available numerical methods for deterministic mathematical programs with complementarity constraints.

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Published date: 2006
Organisations: Operational Research

Identifiers

Local EPrints ID: 79545
URI: http://eprints.soton.ac.uk/id/eprint/79545
ISSN: 1052-6234
PURE UUID: 120b74ed-668f-410c-b9f9-3db7a70e5921
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

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Date deposited: 17 Mar 2010
Last modified: 03 Dec 2019 01:50

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