THE WEIGHTING METHOD AND MULTIOBJECTIVE PROGRAMMING UNDER NEW CONCEPTS OF GENERALIZED (Φ, ρ)-INVEXITY

In the paper, the weighting method is used for solving the considered nonconvex vector optimization problem. The equivalence between a weak Pareto solution of the original vector optimization problem and an optimal solution of its corresponding unconstrained scalar optimization problem is established under (Phi, rho)-invexity. Further, the definition of a differentiable KT-(Phi, rho)-invex vector optimization problem is introduced and the sufficient optimality conditions are established for such nonconvex differentiable multiobjective programming problems. In order to prove several Mond-Weir duality results for a new class of nonconvex differentiable vector optimization problems, the concept of WD-(Phi, rho)-invexity is introduced. It turns out that the results presented in the paper are proved also for such nonconvex vector optimization problems in which not all functions constituting them have the fundamental property of many generalized convexity notions, earlier introduced in the literature.