TY - JOUR
T1 - ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM
AU - Ventura, Estefany Castillo
AU - Papa Quiroz, Erik Alex
N1 - Publisher Copyright:
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024.
PY - 2024/7/1
Y1 - 2024/7/1
N2 - Given the problem of minimizing a possibly nonconvex and nonsmooth function in a real Hilbert space, we present a generalized epsilon-descent algorithm motivated from the abstract descent method introduced by Attouch et al. [Math. Program. 137 (2013) 91–129] with two essential additions, we consider scalar errors on the sufficient descent condition, as well as, on the relative inexact optimality condition. Under general conditions on the function to be minimized, we obtain that all accumulation points of the sequences generated by the algorithm, if they exist, are generalized critical limit points of the objective function.
AB - Given the problem of minimizing a possibly nonconvex and nonsmooth function in a real Hilbert space, we present a generalized epsilon-descent algorithm motivated from the abstract descent method introduced by Attouch et al. [Math. Program. 137 (2013) 91–129] with two essential additions, we consider scalar errors on the sufficient descent condition, as well as, on the relative inexact optimality condition. Under general conditions on the function to be minimized, we obtain that all accumulation points of the sequences generated by the algorithm, if they exist, are generalized critical limit points of the objective function.
KW - coercive function
KW - descent methods
KW - nonconvex optimization
KW - Nonsmooth optimization
KW - relative error
KW - scalar error
UR - http://www.scopus.com/inward/record.url?scp=85203342567&partnerID=8YFLogxK
U2 - 10.1051/ro/2024060
DO - 10.1051/ro/2024060
M3 - Article
AN - SCOPUS:85203342567
SN - 0399-0559
VL - 58
SP - 3417
EP - 3438
JO - RAIRO - Operations Research
JF - RAIRO - Operations Research
IS - 4
ER -