A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints

Ademir A. Ribeiro (), Mael Sachine () and Evelin H. M. Krulikovski
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Ademir A. Ribeiro: Federal University of Paraná
Mael Sachine: Federal University of Paraná
Evelin H. M. Krulikovski: Federal University of Paraná

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 3, No 13, 1067-1083

Abstract: Abstract We propose a comparative study of sequential optimality conditions for mathematical programs with cardinality constraints. Besides analyzing some of the classical approximate conditions for nonlinear programming, such as AKKT, CAKKT and PAKKT, we also propose an approximate weak stationarity ( $${ AW}$$ AW -stationarity) concept designed to deal with this class of problems and we prove that it is a legitimate optimality condition independently of any constraint qualification. We point out that, despite the computational appeal of the sequential optimality conditions, in this work we are not concerned with algorithmic consequences. Our aim is purely to discuss theoretical aspects of such conditions for MPCaC problems.

Keywords: Mathematical programs with cardinality constraints; Sequential optimality conditions; Weak stationarity; Constraint qualification; Nonlinear programming; 90C30; 90C33; 90C46 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02007-0

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