SECOND ORDER DUALITY RESULTS FOR MULTIOBJECTIVE PROGRAMMING PROBLEMS UNDER SECOND ORDER (Φ, ρ)-INVEXITY

In this paper, new generalized invexity concepts for twice differentiable functions are introduced. The so-called second order (Φ, ρ)-invexity generalizes many classes of second order generalized convexity notions existing in the literature. Second order multiobjective dual problems in the format of Mond-Weir and in the format of Wolfe are formulated for the considered differentiable vector optimization problem and several second order duality results are established under second order (Φ, ρ)-invexity. With the reference to the said functions, we extend some results of second order duality for a larger class of vector optimization problems with nonconvex twice differentiable functions.