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

作者：Zhong, Ren-you; Lian, Huan-xia; Fan, Jiang-hua^*

来源：Journal of Optimization Theory and Applications, 2013, 159(2): 341-359.

DOI：10.1007/s10957-013-0342-4

• Optimization problem
• Exceptional family of elements
• Existence of solutions
• Constrained optimization problem
• Convex quadratic programming problem

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.

• 出版日期2013-11
• 单位广西师范大学