Weak sharp minima revisited, part II: application to linear regularity and error bounds

• 成果类型: Article
• 署名作者: Burke, JV; Deng, S
• 署名单位: University of Washington; University of Washington Seattle; Northern Illinois University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0615-2
• 发表日期: 2005
• 页码: 235-261
• 关键词: constraint qualifications; metric regularity; convex; systems

摘要

The notion of weak sharp minima is an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. It has been studied extensively by several authors. This paper is the second of a series on this subject where the basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II we study applications to the linear regularity and bounded linear regularity of a finite collection of convex sets as well as global error bounds in convex programming. We obtain both new results and reproduce several existing results from a fresh perspective.