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

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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 (\({ AW}\)-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.

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Acknowledgements

This work was partially supported by CNPq (Grant 309437/2016-4).

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Authors and Affiliations

  1. Federal University of Paraná, Curitiba, Brazil

    Ademir A. Ribeiro, Mael Sachine & Evelin H. M. Krulikovski

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  1. Ademir A. Ribeiro
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  2. Mael Sachine
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  3. Evelin H. M. Krulikovski
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Correspondence to Ademir A. Ribeiro.

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Communicated by Wei Bian.

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Ribeiro, A.A., Sachine, M. & Krulikovski, E.H.M. A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints. J Optim Theory Appl 192, 1067–1083 (2022). https://doi.org/10.1007/s10957-022-02007-0

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  • DOI: https://doi.org/10.1007/s10957-022-02007-0

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