On reductibility of degenerate optimization problems to regular operator equations
type: Item
instance of: scholarly article
title: On reductibility of degenerate optimization problems to regular operator equations
zbMATH Open document ID: 1379.90036
DOI: 10.1134/S0965542516120058
published in: Computational Mathematics and Mathematical Physics
publication date: 2017-03-28T00:00:00Z
review text: The authors investigate degenerate equality constrained optimization problems on Banach spaces; by degeneracy they mean that the derivative of the constraint function at a solution is not surjective. To reduce such problems to regular systems of equations, they use the \(p\)-regularity theory due to \textit{A. A. Tret'yakov} [Zh. Vychisl. Mat. Mat. Fiz. 24, No. 2, 203--209 (1984; Zbl 0537.49009); Russ. Math. Surv. 42, No. 5, 179--180 (1987; Zbl 0683.58008); translation from Usp. Mat. Nauk 42, No. 5(257), 215--216 (1987)]. The systems so obtained do not involve the objective functions, and their solutions are proved to be locally unique. Applications to mathematical programming problems with complememtarity constraints and to linear programming problems are discussed.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 6697881
zbMATH Keywords: degenerate optimization problems
zbMATH Keywords: \(p\)-regularity
zbMATH Keywords: nonlinear optimization
zbMATH Keywords: complementarity problems
zbMATH Keywords: linear programming
author: Ewa M. Bednarczuk
author: A. Tret'yakov
reviewed by: Juan-Enrique Martínez-Legaz
MaRDI profile type: Publication
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full work available at URL: s0965542516120058
OpenAlex ID: W2565698613
description: scientific article; zbMATH DE number 6697881