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Asymptotic Analysis for a Class of Quasiconvex Semi-Infinite Programming Problems

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  • Stephanie Caro

    (Universidad Arturo Prat)

  • Filip Thiele

    (Universidad de Concepción)

Abstract

We present sufficient conditions to guarantee the existence of solutions for nonconvex semi-infinite optimization problems. These conditions are also employed to establish the lower semicontinuity of the value function at 0. Furthermore, we extend classical results from convex analysis to characterize the global properties of quasiconvex functions based on their behavior at individual points. Our findings generalize and complement existing approaches, addressing problems that extend beyond the scope of previous results.

Suggested Citation

  • Stephanie Caro & Filip Thiele, 2025. "Asymptotic Analysis for a Class of Quasiconvex Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-24, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02821-2
    DOI: 10.1007/s10957-025-02821-2
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    6. Fabián Flores-Bazán & Filip Thiele, 2022. "On the Lower Semicontinuity of the Value Function and Existence of Solutions in Quasiconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 390-417, November.
    7. F. Bonenti & J. E. Martínez-Legaz, 2015. "On the Existence of a Saddle Value," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 785-792, June.
    8. 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.
    9. 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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