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

Title & Authors
SECOND-ORDER UNIVEX FUNCTIONS AND GENERALIZED DUALITY MODELS FOR MULTIOBJECTIVE PROGRAMMING PROBLEMS CONTAINING ARBITRARY NORMS
Zalmai, G.J.;

Abstract
In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\small{\mathcal{F}}$, $\small{b}$, $\small{{\phi}}$, $\small{{\rho}}$, $\small{{\theta}}$)-sounivex functions, ($\small{\mathcal{F}}$, $\small{b}$, $\small{{\phi}}$, $\small{{\rho}}$, $\small{{\theta}}$)-pseudosounivex functions, and ($\small{\mathcal{F}}$, $\small{b}$, $\small{{\phi}}$, $\small{{\rho}}$, $\small{{\theta}}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\small{\mathcal{F}}$, $\small{b}$, $\small{{\phi}}$, $\small{{\rho}}$, $\small{{\theta}}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.
Keywords
multiobjective programming;generalized ($\small{\mathcal{F}}$, b, $\small{{\phi}}$, $\small{{\rho}}$, $\small{{\theta}}$)-sounivex functions;arbitrary norms;dual problems;duality theorems;
Language
English
Cited by
1.
On Second-Order Generalized Convexity, Journal of Optimization Theory and Applications, 2016, 168, 3, 802
2.
Higher-order duality for multiobjective programming problem involving (Φ,ρ)-invex functions, Journal of the Egyptian Mathematical Society, 2015, 23, 1, 12
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