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

S. K. Suneja¹, Sunila Sharma¹, Malti Kapoor²

¹Department of Mathematics, Miranda House, University of Delhi, Delhi, India.
²Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi, India.

DOI: 10.4236/am.2015.61002                

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.

Keywords

Nonsmooth Vector Optimization over Cones, (Weak) Minimizers of Order k, Nonsmooth (F, ρ)-Convex Function of Order k

Conflicts of Interest

The authors declare no conflicts of interest.

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