ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM

Ventura E.C.; Papa Quiroz E.A. · RAIRO - Operations Research (2024) · DOI: 10.1051/ro/2024060

Resumen

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. © The authors. Published by EDP Sciences, ROADEF, SMAI 2024.

Instituciones: Universidad Nacional Mayor de San Marcos; Pontificia Universidad Católica del Perú