A Fritz John theorem in complex space

Abstract

Necessary conditions of the Fritz John type are given for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space.Consider the problem towhere S is a polyhedral cone in, and Cm and f: C2n → C, g : C2n → Cm are differentiable functions. A necessary condition for a feasible point z0 to be optimal is that there exist τ≥0, ν ∈ S*, (τ, ν) ≠ 0, such thatand