an:04096227
Zbl 0669.49012
Bhakta, P. C.; Roychaudhuri, Sumitra
Optimization in Banach spaces
EN
J. Math. Anal. Appl. 134, No. 2, 460-470 (1988).
00169051
1988
j
49K27 90C48
real Banach spaces; closed cone; strict separation axiom; necessary condition
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).
M.Todorov