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

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 $G_{f}$Gf-bonvexity/$G_{f}$Gf-pseudobonvexity assumptions. We construct nontrivial numerical examples which are $G_{f}$Gf-bonvex/$G_{f}$Gf-pseudobonvex but neither η-bonvex/η-pseudobonvex nor η-invex/η-pseudoinvex.

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