Abstract generalized epsilon-descent algorithm

¹ Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas, Lima, Peru
² Pontificia Universidad Católica del Perú, Departamento Académico de Ciencias, San Miguel, Peru

^* Corresponding author: erikpapa@gmail.com

Received: 15 December 2022
Accepted: 6 March 2024

Abstract

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.