TY - JOUR
T1 - Strongly Quasiconvex Functions
T2 - What We Know (So Far)
AU - Grad, Sorin Mihai
AU - Lara, Felipe
AU - Marcavillaca, Raúl T.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2025/5
Y1 - 2025/5
N2 - 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.
AB - 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.
KW - Equilibrium problems
KW - Nonconvex optimization
KW - Proximal point algorithms
KW - Strongly quasiconvex functions
KW - Subgradient methods
UR - https://www.scopus.com/pages/publications/105001494342
U2 - 10.1007/s10957-025-02641-4
DO - 10.1007/s10957-025-02641-4
M3 - Article
AN - SCOPUS:105001494342
SN - 0022-3239
VL - 205
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
M1 - 38
ER -