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Optimization in Banach spaces. (English) Zbl 0669.49012
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
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##### References:
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