Componentwise Dinkelbach algorithm for nonlinear fractional optimization problems

verfasst von: Christian Günther, Alexandru Orzan, Radu Precup
Abstract: The paper deals with fractional optimization problems where the objective function (ratio of two functions) is defined on a Cartesian product of two real normed spaces X and Y. Within this framework, we are interested to determine the so-called partial minimizers, i.e. points in (Formula presented.) with the property that any of its variables minimizes the objective function, restricted to this variable, with respect to the other one. While any global minimizer is obviously a partial minimizer, the reverse implication holds true only under additional assumptions (e.g. separability properties of the involved functions). By exploiting the particularities of the objective function, we deliver a Dinkelbach type algorithm for computing partial minimizers of fractional optimization problems. Further assumptions on the involved spaces and functions, such as Lipschitz-type continuity, partial Fréchet differentiability, and coercivity, enable us to establish the convergence of our algorithm to a partial minimizer.
Organisationseinheit(en): Institut für Angewandte Mathematik
Externe Organisation(en): Babeș-Bolyai University (UBB)
Technical University of Cluj-Napoca
Romanian Academy
Typ: Artikel
Journal: OPTIMIZATION
Band: 73
Seiten: 3323-3337
Anzahl der Seiten: 15
ISSN: 0233-1934
Publikationsdatum: 2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Steuerung und Optimierung, Managementlehre und Operations Resarch, Angewandte Mathematik
Elektronische Version(en): https://doi.org/10.1080/02331934.2023.2256750 (Zugang: Geschlossen)

BibTeX

@article{09a85a7d2c8f449988f7651eb9bd1b0a,
title = "Componentwise Dinkelbach algorithm for nonlinear fractional optimization problems",
abstract = "The paper deals with fractional optimization problems where the objective function (ratio of two functions) is defined on a Cartesian product of two real normed spaces X and Y. Within this framework, we are interested to determine the so-called partial minimizers, i.e. points in (Formula presented.) with the property that any of its variables minimizes the objective function, restricted to this variable, with respect to the other one. While any global minimizer is obviously a partial minimizer, the reverse implication holds true only under additional assumptions (e.g. separability properties of the involved functions). By exploiting the particularities of the objective function, we deliver a Dinkelbach type algorithm for computing partial minimizers of fractional optimization problems. Further assumptions on the involved spaces and functions, such as Lipschitz-type continuity, partial Fr{\'e}chet differentiability, and coercivity, enable us to establish the convergence of our algorithm to a partial minimizer.",
keywords = "coercive function, Dinkelbach type algorithm, Fractional optimization, partial minimizer",
author = "Christian G{\"u}nther and Alexandru Orzan and Radu Precup",
note = "Publisher Copyright: {\textcopyright} 2023 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2024",
doi = "10.1080/02331934.2023.2256750",
language = "English",
volume = "73",
pages = "3323--3337",
journal = "OPTIMIZATION",
issn = "0233-1934",
publisher = "Taylor and Francis Ltd.",
number = "11",
}