Relaxation methods with step regulation for solving constrained optimization problems
type: Item
instance of: scholarly article
title: Relaxation methods with step regulation for solving constrained optimization problems
zbMATH Open document ID: 0917.49028
DOI: 10.1007/BF02367672
author: Z. R. Gabidullina
published in: Journal of Mathematical Sciences (New York)
publication date: 1996-06-30T00:00:00Z
full work available at URL: https://eudml.org/doc/69123
review text: We study the problem \[ \min_{x\in D} f(x),\tag{1} \] where \(f(x)\) is a continuously differentiable pseudoconvex function satisfying Condition A (introduced in [\textit{Z. R. Gabidulinna}, J. Sov. Math. 50, No. 5, 1803-1809 (1990); translation from Issled. Prikl. Mat. 14, 15-25 (1987; Zbl 0706.90061)]): A continuous function \(f\) satisfies Condition A on the set \(D\) if there exists \(\kappa>0\) such that \[ f(\alpha x+(1- \alpha)y)\geq \alpha f(x)+ (1-\alpha) f(y)- \alpha(1- \alpha)\kappa\| x-y\|^2\;\forall x,y\in D,\;\forall\alpha\in [0,1]. \] We propose a relaxation method for solving the problem (1). Depending on the method of choosing the size of the recursion step, one can obtain various versions of the algorithm.
Mathematics Subject Classification ID: 49M20
Mathematics Subject Classification ID: 90C26
zbMATH DE Number: 894497
zbMATH Keywords: constrained optimization
zbMATH Keywords: continuously differentiable pseudoconvex function
zbMATH Keywords: relaxation method
MaRDI profile type: Publication
Wikidata QID: Q58336430
cites work: Q3474487
cites work: Lower subdifferentiable functions and their minimization by cutting planes
description: scientific article; zbMATH DE number 894497