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A Quasiconvex Asymptotic Function with Applications in Optimization

Author

Listed:
  • Nicolas Hadjisavvas

    (University of the Aegean
    King Fahd University of Petroleum and Minerals)

  • Felipe Lara

    (Universidad de Tarapacá)

  • Juan Enrique Martínez-Legaz

    (Universitat Autònoma de Barcelona
    Barcelona Graduate School of Mathematics (BGSMath))

Abstract

We introduce a new asymptotic function, which is mainly adapted to quasiconvex functions. We establish several properties and calculus rules for this concept and compare it to previous notions of generalized asymptotic functions. Finally, we apply our new definition to quasiconvex optimization problems: we characterize the boundedness of the function, and the nonemptiness and compactness of the set of minimizers. We also provide a sufficient condition for the closedness of the image of a nonempty closed and convex set via a vector-valued function.

Suggested Citation

  • Nicolas Hadjisavvas & Felipe Lara & Juan Enrique Martínez-Legaz, 2019. "A Quasiconvex Asymptotic Function with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 170-186, January.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1317-2
    DOI: 10.1007/s10957-018-1317-2
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    References listed on IDEAS

    as
    1. Alberto Cambini & Laura Martein, 2009. "Generalized Convexity and Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-70876-6, October.
    2. S. Deng, 1998. "Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 123-131, January.
    3. Fabián Flores-Bazán & Fernando Flores-Bazán & Cristián Vera, 2015. "Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives," Journal of Global Optimization, Springer, vol. 63(1), pages 99-123, September.
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    Cited by:

    1. Nicolas Hadjisavvas & Felipe Lara & Dinh The Luc, 2020. "A general asymptotic function with applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 78(1), pages 49-68, September.
    2. Felipe Lara, 2020. "Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 134-150, April.
    3. Alfredo Iusem & Felipe Lara, 2019. "Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 122-138, October.

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