On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions

Abstract

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)−ρ −(η,θ)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved.

Keywords

• multiobjective fractional programming
• Clarke gradient
• (p,r)−ρ−(η,θ)-invexity
• efficiency
• sufficient optimality conditions
• duality theorems