Abstract generalized epsilon-descent algorithm
DOI:
https://doi.org/10.15381/pesquimat.v25i2.24364Keywords:
Non-smooth optimization, non-convex optimization, coercive function, descent methods, relative error, scalar errorsAbstract
Given the problem of minimizing a possibly non-convex and non-smooth function in Euclidean space, we present an abstract generalized ϵ-descent algorithm. This algorithm is motivated by the abstract convergence of descent methods introduced by Attouch et al. section 2 (Math Program Ser A, 137: 91-129, 2013) with one essential difference, we consider scalar errors in each approximation. As a result, we obtain that all accumulation points of the sequences generated by algorithms satisfying the conditions of the abstract algorithm are generalized critical limit points.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Estéfany Castillo Ventura, Erik Alex Papa Quiroz
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
THE AUTHORS RETAIN THEIR RIGHTS:
a) The authors retain their trademark and patent rights, and also on any process or procedure described in the article.
b) The authors retain the right to share, copy, distribute, execute and publicly communicate the article published in Pesquimat magazine (for example, place it in an institutional repository or publish it in a book), with recognition of its initial publication in the Pesquimat magazine.
c) The authors retain the right to make a later publication of their work, to use the article or any part of it (for example: a compilation of their works, notes for conferences, thesis, or for a book), provided that they indicate the source of publication (authors of the work, magazine, volume, number and date).
