Metric projection onto a closed set: Necessary and sufficient conditions for the global minimum

• 成果类型: Article
• 署名作者: Mohebi, H; Rubinov, A
• 署名单位: Shahid Bahonar University of Kerman (SBUK); Federation University Australia
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1050.0173
• 发表日期: 2006
• 页码: 124-132
• 关键词: optimality conditions; downward sets

摘要

Necessary and sufficient conditions for a local minimum form a well-developed chapter of optimization theory. Determination of such conditions for the global minimum is a challenging problem. Useful conditions are currently known only for a few classes of nonconvex optimization problems. It is important to find different classes of problems for which the required conditions can be obtained. In this paper we examine one of these classes: the minimization of the distance to an arbitrary closed set in a class of ordered normed spaces. We use the structure of the objective function in order to present necessary and sufficient conditions that give a clear understanding of the structure of a global minimizer and can be easily verified for some problems under consideration.