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Strongly Quasiconvex Functions: What We Know (So Far)

Author

Listed:
  • Sorin-Mihai Grad

    (Unité de Mathématiques Appliquées, ENSTA Paris, Institut Polytechnique de Paris)

  • Felipe Lara

    (Universidad de Tarapacá)

  • Raúl T. Marcavillaca

    (Universidad de Chile)

Abstract

Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a nonnegative strongly convex numerator and a concave and positive denominator. This survey collects the vast majority of the results involving strongly quasiconvex functions available in the literature at the moment, presenting, in particular, algorithms for minimizing such functions, and suggests some directions where additional investigations would be welcome.

Suggested Citation

  • Sorin-Mihai Grad & Felipe Lara & Raúl T. Marcavillaca, 2025. "Strongly Quasiconvex Functions: What We Know (So Far)," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-41, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02641-4
    DOI: 10.1007/s10957-025-02641-4
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