New class of G-Wolfe-type symmetric duality model and duality relations under G f $G_{f}$ -bonvexity over arbitrary cones

Abstract

Abstract This paper is devoted to theoretical aspects in nonlinear optimization, in particular, duality relations for some mathematical programming problems. In this paper, we introduce a new generalized class of second-order multiobjective symmetric G-Wolfe-type model over arbitrary cones and establish duality results under G f $G_{f}$ -bonvexity/ G f $G_{f}$ -pseudobonvexity assumptions. We construct nontrivial numerical examples which are G f $G_{f}$ -bonvex/ G f $G_{f}$ -pseudobonvex but neither η-bonvex/η-pseudobonvex nor η-invex/η-pseudoinvex.

Keywords

• Second-order
• Multiobjective
• Efficient solution
• Wolfe
• G f $G_{f}$ -Bonvexity/ G f $G_{f}$ -pseudobonvexity