ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM

Estefany Castillo Ventura; Erik Alex Papa Quiroz

doi:10.1051/ro/2024060

ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM

Estefany Castillo Ventura
, Erik Alex Papa Quiroz

Universidad Nacional Mayor de San Marcos
Pontificia Universidad Católica del Perú

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3417-3438
Number of pages	22
Journal	RAIRO - Operations Research
Volume	58
Issue number	4
DOIs	https://doi.org/10.1051/ro/2024060
State	Published - 1 Jul 2024
Externally published	Yes

Keywords

Nonsmooth optimization
coercive function
descent methods
nonconvex optimization
relative error
scalar error

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10.1051/ro/2024060

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title = "ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM",

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.",

keywords = "Nonsmooth optimization, coercive function, descent methods, nonconvex optimization, relative error, scalar error",

author = "Ventura, \{Estefany Castillo\} and \{Papa Quiroz\}, \{Erik Alex\}",

note = "Publisher Copyright: {\textcopyright} The authors. Published by EDP Sciences, ROADEF, SMAI 2024.",

year = "2024",

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doi = "10.1051/ro/2024060",

language = "English",

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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 - Nonsmooth optimization

KW - coercive function

KW - descent methods

KW - nonconvex optimization

KW - relative error

KW - scalar error

UR - https://www.scopus.com/pages/publications/85203342567

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 -

ABSTRACT GENERALIZED EPSILON-DESCENT ALGORITHM

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Keywords

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