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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    2,915 Downloads   3,422 Views   Citations


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.

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The authors declare no conflicts of interest.

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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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