A smoothing method for mathematical programs with equilibrium constraints
type: Item
instance of: scholarly article
title: A smoothing method for mathematical programs with equilibrium constraints
zbMATH Open document ID: 0959.65079
author: Francisco Facchinei
author: Houyuan Jiang
author: Liqun Qi
published in: Mathematical Programming. Series A. Series B
publication date: 1999-06-28T00:00:00Z
review text: The authors propose an algorithm for solving optimization problems whose constraints include a strongly monotone variational inequality. Their idea is to reformulate the considered problem as a one-level nonsmoothly constrained optimization problem \((P)\) by using the Karush-Kuhn-Tucker conditions for the variational inequality. Next, they introduce a sequence \((P_{\mu^k})\) of smooth, regular one-level problems which progressively approximate the nonsmooth problem \((P)\). It is proved that the sequence of solutions of the problems \((P_{\mu^k})\) is contained in a compact set and that each of its limit points is a solution of the original problem. Furthermore, it is shown that the sequence of stationary points of the problems \((P_{\mu^k})\) is also contained in a compact set and that its limit points furnish strongly \(C\)-stationary points of the original problem.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 1309160
zbMATH Keywords: smoothing method
zbMATH Keywords: equilibrium constraints
zbMATH Keywords: variational inequality problems
zbMATH Keywords: strong monotonicity
zbMATH Keywords: optimality conditions
zbMATH Keywords: global convergence
zbMATH Keywords: algorithm
reviewed by: Wolfgang W. Breckner
MaRDI profile type: Publication
full work available at URL: s101070050048
OpenAlex ID: W4246495354
DOI: 10.1007/S101070050048
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description: scientific article; zbMATH DE number 1309160