Optimization in Banach spaces
type: Item
instance of: scholarly article
title: Optimization in Banach spaces
zbMATH Open document ID: 0669.49012
DOI: 10.1016/0022-247X(88)90035-2
author: P. C. Bhakta
author: Sumitra Roychaudhuri
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: Let X and Y be real Banach spaces and \(K\subset Y\) a closed cone satisfying some additional conditions, which generates a partial ordering in Y. The authors consider the abstract optimization problem: (MP) Minimise f(x) subject to g(x)\(\geq 0\) and \(h(x)=0\), where f:X\(\to Y\), \(g:X\to Y^ m\) and \(h:X\to Y^ p\). Using so called ``strict separation axiom'' they establish a Fritz John and Kuhn-Tucker-type necessary condition for the existence of a solution to the problem (MP).
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 4096227
zbMATH Keywords: real Banach spaces
zbMATH Keywords: closed cone
zbMATH Keywords: strict separation axiom
zbMATH Keywords: necessary condition
reviewed by: Maxim Ivanov Todorov
MaRDI profile type: Publication
cites work: Q4135211
cites work: Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space
cites work: Q5332416
cites work: Optimization theory in linear spaces. I
cites work: Optimization theory in linear spaces. II: On systems of linear operator inequalities in partially ordered normed linear spaces
cites work: Optimization theory in linear spaces. III: Mathematical programming in partially ordered Banach spaces
cites work: Nonlinear Programming in Banach Space
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description: scientific article; zbMATH DE number 4096227