Constraint qualifications and optimality conditions for optimization problems with cardinality constraints

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• 作者：Michal Červinka ; Christian Kanzow ; Alexandra Schwartz
• 关键词：Cardinality constraints ; Constraint qualifications ; Optimality conditions ; KKT conditions ; Strongly stationary points
• 刊名：Mathematical Programming
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：160
• 期：1-2
• 页码：353-377
• 全文大小：618 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646
• 卷排序：160

文摘

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.