Journal of the
Korean Mathematical Society JKMS

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

Keywords: multiobjective programming, generalized $(\mathcal{F},b,\phi,\rho,\theta)$-sounivex functions, arbitrary norms, dual problems, duality theorems

MSC numbers: Primary 90C29, 90C30; Secondary 49M15, 90C26