TY - JOUR
T1 - A subgradient projection method for quasiconvex minimization
AU - Choque, Juan
AU - Lara, Felipe
AU - Marcavillaca, Raúl T.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
PY - 2024/11
Y1 - 2024/11
N2 - In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By employing strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous, and strongly quasiconvex function (in the sense of Polyak in Soviet Math 7:72–75, 1966), under the same assumptions as those required for convex functions with the convex subdifferentials. Furthermore, a quasi-linear convergence rate of the iterates, extending similar results for the general quasiconvex case, is also provided.
AB - In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By employing strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous, and strongly quasiconvex function (in the sense of Polyak in Soviet Math 7:72–75, 1966), under the same assumptions as those required for convex functions with the convex subdifferentials. Furthermore, a quasi-linear convergence rate of the iterates, extending similar results for the general quasiconvex case, is also provided.
KW - 49M37
KW - 90C26
KW - 90C30
KW - First-order methods
KW - Generalized convexity
KW - Nonconvex optimization
KW - Quasiconvexity
KW - Subgradient methods
UR - https://www.scopus.com/pages/publications/85203252339
U2 - 10.1007/s11117-024-01082-z
DO - 10.1007/s11117-024-01082-z
M3 - Article
AN - SCOPUS:85203252339
SN - 1385-1292
VL - 28
JO - Positivity
JF - Positivity
IS - 5
M1 - 64
ER -