A Different Approach to Cone-Convex Optimization
A Different Approach to Cone-Convex Optimization作者机构：Department of Mathematics Miranda House College University of Delhi Delhi India Department of Mathematics Moti Lal Nehru College (M) University of Delhi Delhi India
出 版 物：《American Journal of Operations Research》 (美国运筹学期刊（英文）)
年 卷 期：2013年第3卷第6期
页 面：536-541页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Convex Optimization Cone-Convex Functions KKT Conditions Duality
摘 要：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.
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