Strongly Quasiconvex Functions: What We Know (So Far)

Sorin-Mihai Grad (), Felipe Lara () and Raúl T. Marcavillaca ()
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Sorin-Mihai Grad: Unité de Mathématiques Appliquées, ENSTA Paris, Institut Polytechnique de Paris
Felipe Lara: Universidad de Tarapacá
Raúl T. Marcavillaca: Universidad de Chile

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 19, 41 pages

Abstract: 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.

Keywords: Strongly quasiconvex functions; Proximal point algorithms; Equilibrium problems; Nonconvex optimization; Subgradient methods (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02641-4

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