Higher Order Optimality and Duality in Vector Optimization

In section 4.1 a new class of higher order (F,ρi, σj)type I functions are introduced for a vector minimization problem. Various known generalized invex functions such as type-I, second order type-I and second order (F,ρi,σj)-type I are particular cases of higher order (F, ρi, σj)-type I functions. This class of functions is used to establish higher order duality results for a nondifferentiable multiobjective fractional programming problem whose objective functions and constraints contain support functions of compact convex sets in n R . Higher order Mond-Weir type and Schaible type duals are formulated for the multiobjective fractional program and various duality results are established. It has been observed that these primal and dual pairs when appropriately specialized, reduce to the classes of problems with multiple, fractional, and conventional objective functions considered in [57], [58], [59], [161], and [163].