Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, part I: Theory
Abstract
Necessary and sufficient saddle-point-and stationary-point-type proper efficiency conditions are established for a class of nonsmooth nonconvex multiobjective fractional programming problems with operator constraints on a real locally convex topological vector space. Furthermore, utilizing these efficiency results, seven multiobjective dual problems are formulated and appropriate duality theorems are proved. These optimality and duality criteria also contain as special cases similar results for three classes of problems with multiple, fractional, and conventional objective functions, which are particular cases of the main optimization model considered in this paper. As a nontrivial illustration of the form and contents of the results developed in this paper, various proper efficiency conditions and duality models are derived for a class of continuous-time multiobjective fractional programming problems with operator constraints.
