Title: Smoothing mathematical programmes with equilibrium constraints via neural network function

Authors: Mohamed A. Tawhid

Addresses: Department of Mathematics and Statistics, School of Advanced Technologies and Mathematics, Thompson Rivers University, 900 McGill Road, P.O. Box 3010, Kamloops, BC V2C 5N3, Canada

Abstract: We propose a smoothing approach based on neural network function to solve a mathematical programme with equilibrium constraints (MPEC) in which the constraints are defined by a parametric variational inequality (PVI). We reformulate MPEC as an equivalent one level non-smooth optimisation problem. Then, this non-smooth optimisation problem will transfer to a sequence of smooth optimisation problems that can be solved by standard available software for constrained optimisation. Our results obtained in this paper continue to hold for any mathematical programme with parametric nonlinear complementarity/mixed complementarity constraints. Also, we test the performance of the proposed smoothing approach on a set of well-known problems and give some comparisons between our approach and other smoothing approaches. We are hoping our smoothing approach via neural network function will provide a basis for future applications work in this area, and generate some dynamic interactions between algorithmic developers and modellers/practitioners in the MPEC field.

Keywords: mathematical programmes; equilibrium constraints; MPEC; parametric variational inequality; optimality conditions; bilevel optimisation; smoothing methods; neural networks; online solvers.

DOI: 10.1504/IJOR.2010.035042

International Journal of Operational Research, 2010 Vol.9 No.2, pp.141 - 159

Published online: 01 Sep 2010 *

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