Complex Fractional Programming Involving Generalized Quasi/Pseudo Convex Functions
H.C. Lai, J. C. Liu · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2002
Consider a nondifferentiable complex fractional programming where f, g : C2n → C and h : C2n → Cm are analytic functions, A, B ∈ Cn × n are positive semidefinite Hermitian matrices, S is a polyhedral cone in Cm. In this paper, we establish conditions for the existence of an optimal solution in (P) involving (ℒ︁, ρ, θ)-quasiconvex/-pseudoconvex analytic functions. Based on the sufficient optimality theorem, we construct a duality model and then establish weak/strong, and strict converse duality theorems.