Author(s)

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.

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.

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

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.