Sufficiency and duality for nonsmooth multiobjective fractional programming problems involving $$(\Phi ,\rho ,\alpha )$$ ( Φ , ρ , α ) -V-invexity

Abstract

In this paper, we consider a class of nonsmooth multiobjective fractional programming problems in which the involved functions are locally Lipschitz. A new concept of invexity for locally Lipschitz vector-valued functions is introduced, called \((\Phi ,\rho ,\alpha )\)-V-invexity. Based upon the \((\Phi ,\rho ,\alpha )\)-V-invex functions, the optimality conditions for a feasible solulion to be an efficient solution are derived. Weak, strong, and strict converse duality theorems for Mond–Weir type dual are also proved under the aforesaid functions.