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

  • Zalmai, G.J. (Department of Mathematics and Computer Science, Northern Michigan University)
  • Received : 2010.05.16
  • Published : 2013.07.01

Abstract

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity 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

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