J. Korean Math. Soc. 2013; 50(4): 727-753
Printed July 1, 2013
https://doi.org/10.4134/JKMS.2013.50.4.727
Copyright © The Korean Mathematical Society.
G. J. Zalmai
Northern Michigan University
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
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