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Higher-Order Minimizers and Generalized (F,ρ)-Convexity in Nonsmooth Vector Optimization over Cones

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DOI: 10.4236/am.2015.61002    2,830 Downloads   3,271 Views   Citations

ABSTRACT

In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Suneja, S. , Sharma, S. and Kapoor, M. (2015) Higher-Order Minimizers and Generalized (F,ρ)-Convexity in Nonsmooth Vector Optimization over Cones. Applied Mathematics, 6, 7-19. doi: 10.4236/am.2015.61002.

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