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Mas-Colell Properness Condition and Almost Convexity in Nonconvex Optimization

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  • Fabián Flores-Bazán

    (Universidad de Concepción)

Abstract

In last years practitioners and theorists are paying attention on general nonconvex optimization problems due to the presence of modern tools to face such problems. Our focus in this paper is dealing with the infinite dimensional setting. Firstly, associated to two different concepts of interiority, we introduce two notions of almost convexity, and establish some relationships between the function itself and its lower semicontinuous hull. Another important issue in the study of optimization problems is to know when the Fenchel subdifferential of a given nonconvex function at a reference point is nonempty. This property is analyzed in terms of the properness condition introduced, in the context of mathematical economics, by Mas-Colell. Applications to provide necessary and/or sufficient conditions for the fulfillment of strong duality property are given.

Suggested Citation

  • Fabián Flores-Bazán, 2025. "Mas-Colell Properness Condition and Almost Convexity in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-25, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02677-6
    DOI: 10.1007/s10957-025-02677-6
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    References listed on IDEAS

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    5. Fabián Flores-Bazán & William Echegaray & Fernando Flores-Bazán & Eladio Ocaña, 2017. "Primal or dual strong-duality in nonconvex optimization and a class of quasiconvex problems having zero duality gap," Journal of Global Optimization, Springer, vol. 69(4), pages 823-845, December.
    6. G. Mastroeni, 2010. "Some applications of the image space analysis to the duality theory for constrained extremum problems," Journal of Global Optimization, Springer, vol. 46(4), pages 603-614, April.
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