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Higher-Order Minimizers and Generalized (F,<i>ρ</i>)-Convexity in Nonsmooth Vector Optimization over Cones
Department of Mathematics, Miranda House, University of Delhi, Delhi, India
Department of Mathematics, Miranda House, University of Delhi, Delhi, India
Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi, India
- 1 Department of Mathematics, Miranda House, University of Delhi, Delhi, India
- 2 Department of Mathematics, Miranda House, University of Delhi, Delhi, India
- 3 Department of Mathematics, Motilal Nehru College, University of Delhi, Delhi, India
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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.
KeywordsNonsmooth Vector Optimization over Cones(Weak) Minimizers of Order <i>k</i>Nonsmooth (F<i>ρ</i>)-Convex Function of Order k
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