Optimization in Banach spaces. (English) Zbl 0669.49012

Bhakta, P. C.; Roychaudhuri, Sumitra

J. Math. Anal. Appl. 134, No. 2, 460-470 (1988).

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).

Reviewer: M.Todorov

MSC:

49K27	Optimality conditions for problems in abstract spaces
90C48	Programming in abstract spaces

Keywords:

real Banach spaces; closed cone; strict separation axiom; necessary condition

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