A sublinear functional based approximated equivalence to optimality and duality for multiobjective programming in complex spaces

Abstract

In this paper, we introduce a new approximation approach for a class of multiobjective programming problems in complex spaces and their duals. Using a sublinear functional, an approximated problem is constructed at a given feasible solution of the original problem. The equivalence between the solution of the considered multiobjective complex programming problem and its approximated problem is established by deriving the sufficiency theorem under the F-convexity assumption. An example showing this equivalence is also presented. Further, corresponding to the approximated problem, the Mond–Weir and Wolfe-type approximated dual problems are formulated. The duality results for the Mond–Weir and Wolfe-type dual problems are derived using the duality results established for the approximated Mond–Weir and Wolfe-type dual problems, respectively. The importance of the optimality conditions and proposed approximation approach is highlighted in a blind equalization problem in a communication system.