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Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints

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Abstract

In this study, a novel sequential optimality condition for general continuous optimization problems is established. In the context of mathematical programs with equilibrium constraints, the condition is proved to ensure Clarke stationarity. Originally devised for constrained nonsmooth optimization, the proposed sequential optimality condition addresses the domain of the constraints instead of their images, capturing indistinctly the features of the complementarity and the ordinary constraints of optimization problems modeling equilibrium conditions.

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Acknowledgements

This study was supported by Brazilian Funding Agencies Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP (Grants 2018/24293-0, 2016/22989-2 and 2013/07375-0) and Conselho Nacional de Desenvolvimento Cientí-fico e Tecnológico—CNPq (Grants 311476/2014-7 and 302915/2016-8). The authors are also thankful to the anonymous reviewer for providing insightful elements that improved the presentation of this work.

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Authors and Affiliations

  1. University of São Paulo, São Carlos, SP, Brazil

    Elias S. Helou

  2. University of Campinas, Campinas, SP, Brazil

    Sandra A. Santos & Lucas E. A. Simões

Authors
  1. Elias S. Helou
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  2. Sandra A. Santos
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  3. Lucas E. A. Simões
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Correspondence to Lucas E. A. Simões.

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Communicated by Qamrul Hasan Ansari.

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Helou, E.S., Santos, S.A. & Simões, L.E.A. Analysis of a New Sequential Optimality Condition Applied to Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl 185, 433–447 (2020). https://doi.org/10.1007/s10957-020-01658-1

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  • DOI: https://doi.org/10.1007/s10957-020-01658-1

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