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First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization

Author

Listed:
  • F. Flores-Bazán

    (Universidad de Concepción)

  • N. Hadjisavvas

    (King Fahd University of Petroleum and Minerals)

  • F. Lara

    (Universidad de Tarapacá)

  • I. Montenegro

    (Universidad de Concepción)

Abstract

We use asymptotic analysis to describe in a more systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the first- and second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.

Suggested Citation

  • F. Flores-Bazán & N. Hadjisavvas & F. Lara & I. Montenegro, 2016. "First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 372-393, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0938-6
    DOI: 10.1007/s10957-016-0938-6
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    References listed on IDEAS

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    1. 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.
    2. John Cotrina & Fernanda Raupp & Wilfredo Sosa, 2015. "Semi-continuous quadratic optimization: existence conditions and duality scheme," Journal of Global Optimization, Springer, vol. 63(2), pages 281-295, October.
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    Cited by:

    1. 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.
    2. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    3. F. Lara, 2017. "Second-order asymptotic analysis for noncoercive convex optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 469-483, December.

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