Typical convex program is very well posed

• 成果类型: Article
• 署名作者: Ioffe, A; Lucchetti, RE
• 署名单位: Technion Israel Institute of Technology; Polytechnic University of Milan
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0625-0
• 发表日期: 2005
• 页码: 483-499
• 关键词: Optimization; calculus

摘要

In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and right-hand side perturbation of the constraints, while the core'' cost function and the left-hand side constraint functions are kept fixed. The main result shows that the set of the problems which are not well-posed is sigma-porous in a certain strong sense. Our results concern both the infinite and finite dimensional case. In the last case the conclusions are significantly sharper.