Constraint qualifications and optimality conditions for optimization problems with cardinality constraints
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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.
KeywordsCardinality constraints Constraint qualifications Optimality conditions KKT conditions Strongly stationary points
Mathematics Subject Classification90C30 90C11 90B80 90C46
The authors would like to thank both referees for their very detailed comments which helped quite a bit to improve the presentation of the paper.
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