Exceptional Families of Elements for Optimization Problems in Reflexive Banach Spaces with Applications

Ren-you Zhong, Huan-xia Lian and Jiang-hua Fan ()
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Ren-you Zhong: Guangxi Normal University
Huan-xia Lian: Guangxi Normal University
Jiang-hua Fan: Guangxi Normal University

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 2, No 3, 359 pages

Abstract: Abstract In this paper, we propose a new notion of ‘exceptional family of elements’ for convex optimization problems. By employing the notion of ‘exceptional family of elements’, we establish some existence results for convex optimization problem in reflexive Banach spaces. We show that the nonexistence of an exceptional family of elements is a sufficient and necessary condition for the solvability of the optimization problem. Furthermore, we establish several equivalent conditions for the solvability of convex optimization problems. As applications, the notion of ‘exceptional family of elements’ for convex optimization problems is applied to the constrained optimization problem and convex quadratic programming problem and some existence results for solutions of these problems are obtained.

Keywords: Optimization problem; Exceptional family of elements; Existence of solutions; Constrained optimization problem; Convex quadratic programming problem (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-013-0342-4

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