Monotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems
type: Item
instance of: scholarly article
title: Monotonicity of Mangasarian's iterative algorithm for generalized linear complementarity problems
zbMATH Open document ID: 0689.65042
DOI: 10.1016/0022-247X(89)90347-8
author: M. Sun
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Discretization of the Hamilton-Jacobi-Bellman equations of control theory leads to a generalized linear complementary problem (GLCP) of the form \(A_ jx+q_ j\geq 0,\) \(j=1,2,...,m,\) \(\min \{A_ jx+q_ j*\quad j=1,2,...,m\}=0.\) The author extend \textit{O. L. Mangasarian}'s iterative algorithm [J. Optimization Theory Appl. 22, 465-485 (1977; Zbl 0341.65049)] for linear complementarity problems to GLCP. He imposes some additional conditions on the initial point \(x_ 0\) in order to get the monotonicity of the subsequent iterates. As a consequence of the monotonicity the convergence of the method is obtained. The algorithm has been tested on a singular stochastic control problem.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4129904
zbMATH Keywords: generalized linear complementary problem
zbMATH Keywords: iterative algorithm
zbMATH Keywords: convergence
zbMATH Keywords: singular stochastic control problem
reviewed by: S. M. Grzegórski
MaRDI profile type: Publication
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full work available at URL: 0022-247x(89)90347-8
OpenAlex ID: W2004250389
description: scientific article; zbMATH DE number 4129904