Optimization in Banach spaces (Q1118807)

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).