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Horizon and Recession Asymptotic Notions for Sets and Mappings: A Unified Approach

Author

Listed:
  • Yboon García

    (Universidad del Pacífico)

  • Bruno Goicochea

    (Instituto de Matemática y Ciencias Afines (IMCA), Programa de Maestría en Matemática Aplicada)

  • Rubén López

    (Universidad de Tarapacá)

  • Javier Martínez

    (Universidad de Tarapacá, Programa de Doctorado en Ciencias con Mención en Matemática)

Abstract

The aim of this paper is to develop a unified theory of horizon and recession asymptotic notions for sets, functions, and multifunctions. This unified approach allows to exploit both the algebraic and topological features of these objects. We study the notion of regular set defined as a set for which its horizon and recession cones coincide. This notion plays an important role in the theory. Regular functions and multifunctions are defined and studied as well. By using the unified approach, we obtain properties, formulas, calculus rules, and relationships for horizon and recession notions. Finally, we study the horizon and recession mappings of various important functions and multifunctions from variational analysis.

Suggested Citation

  • Yboon García & Bruno Goicochea & Rubén López & Javier Martínez, 2025. "Horizon and Recession Asymptotic Notions for Sets and Mappings: A Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-31, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02655-y
    DOI: 10.1007/s10957-025-02655-y
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    References listed on IDEAS

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    1. Petra Weidner, 2017. "Gerstewitz Functionals on Linear Spaces and Functionals with Uniform Sublevel Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 812-827, June.
    2. J. M. Borwein, 1983. "Adjoint Process Duality," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 403-434, August.
    3. Regina S. Burachik & Alfredo N. Iusem, 2008. "Set-Valued Mappings and Enlargements of Monotone Operators," Springer Optimization and Its Applications, Springer, number 978-0-387-69757-4, March.
    4. Felipe Lara & Rubén López, 2017. "Formulas for Asymptotic Functions via Conjugates, Directional Derivatives and Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 793-811, June.
    5. 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.
    6. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
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