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Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints
Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints
In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739–760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example
stochastic mathematical program with equilibrium constraints, monte carlo/quasi-monte carlo methods, penalization
1432-2994
423-441
Lin, Gui-Hua
9c0a405f-5e2a-4d01-a6eb-a2401295ce2b
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Fukushima, Masao
b542d8b9-7670-4ad2-bd85-240d7e6192e8
Lin, Gui-Hua
9c0a405f-5e2a-4d01-a6eb-a2401295ce2b
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Fukushima, Masao
b542d8b9-7670-4ad2-bd85-240d7e6192e8

Lin, Gui-Hua, Xu, Huifu and Fukushima, Masao (2008) Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints. Mathematical Methods of Operations Research, 67 (3), 423-441. (doi:10.1007/s00186-007-0201-x).

Record type: Article

Abstract

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739–760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example

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More information

Published date: June 2008
Keywords: stochastic mathematical program with equilibrium constraints, monte carlo/quasi-monte carlo methods, penalization
Organisations: Operational Research

Identifiers

Local EPrints ID: 79540
URI: http://eprints.soton.ac.uk/id/eprint/79540
ISSN: 1432-2994
PURE UUID: 9207220d-34e6-4a90-915d-7ae722333459
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

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

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Contributors

Author: Gui-Hua Lin
Author: Huifu Xu ORCID iD
Author: Masao Fukushima

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