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

Applied Mathematics 2015年第1期6卷 7-19页

作者： S. K. Suneja sunila sharma Malti Kapoor Department of Mathematics Miranda House University of Delhi Delhi India Department 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.

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

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A Different Approach to Cone-Convex Optimization

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American Journal of Operations Research 2013年第6期3卷 536-541页

作者： Surjeet Kaur Suneja sunila sharma Meetu B. Grover Malti Kapoor Department of Mathematics Miranda House College University of Delhi Delhi India Department of Mathematics Moti Lal Nehru College (M) University of Delhi Delhi India

In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established.

关键词： Convex Optimization Cone-Convex Functions KKT Conditions Duality

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