Constraint qualifications and optimality conditions for optimization problems with cardinality constraints

• 成果类型: Article
• 署名作者: Cervinka, Michal; Kanzow, Christian; Schwartz, Alexandra
• 署名单位: Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Charles University Prague; University of Wurzburg; Technical University of Darmstadt
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-0986-6
• 发表日期: 2016
• 页码: 353-377
• 关键词: linear-dependence condition; mathematical programs; stationarity

摘要

This paper considers optimization problems with cardinality constraints. Based on a recently introduced reformulation of this problem as a nonlinear program with continuous variables, we first define some problem-tailored constraint qualifications and then show how these constraint qualifications can be used to obtain suitable optimality conditions for cardinality constrained problems. Here, the (KKT-like) optimality conditions hold under much weaker assumptions than the corresponding result that is known for the somewhat related class of mathematical programs with complementarity constraints.