Abstract
(P) minimize Re'f(z, z) + (z H Az) 1/2 ]/Re[g(z, z) - (z H Bz)1/2] subject to h(z, z) ∈ S ⊂ C m , z ∈ C m , where f, g: C 2n → C and h: C 2n → C m are analytic functions, A, B ∈ C m×n are positive semidefinite Hermitian matrices, S is a polyhedral cone in C m . In this paper, we establish conditions for the existence of an optimal solution in (P) involving (£, p, 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.
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