SECOND-ORDER UNIVEX FUNCTIONS AND GENERALIZED DUALITY MODELS FOR MULTIOBJECTIVE PROGRAMMING PROBLEMS CONTAINING ARBITRARY NORMS

Abstract

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, (<TEX>$\mathcal{F}$</TEX>, <TEX>$b$</TEX>, <TEX>${\phi}$</TEX>, <TEX>${\rho}$</TEX>, <TEX>${\theta}$</TEX>)-sounivex functions, (<TEX>$\mathcal{F}$</TEX>, <TEX>$b$</TEX>, <TEX>${\phi}$</TEX>, <TEX>${\rho}$</TEX>, <TEX>${\theta}$</TEX>)-pseudosounivex functions, and (<TEX>$\mathcal{F}$</TEX>, <TEX>$b$</TEX>, <TEX>${\phi}$</TEX>, <TEX>${\rho}$</TEX>, <TEX>${\theta}$</TEX>)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized (<TEX>$\mathcal{F}$</TEX>, <TEX>$b$</TEX>, <TEX>${\phi}$</TEX>, <TEX>${\rho}$</TEX>, <TEX>${\theta}$</TEX>)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.