Componentwise Dinkelbach algorithm for nonlinear fractional optimization problems

authored by
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.

Organisation(s)
Institute of Applied Mathematics
External Organisation(s)
Babeş-Bolyai University (UBB)
Technical University of Cluj-Napoca
Romanian Academy
Type
Article
Journal
OPTIMIZATION
Volume
73
Pages
3323-3337
No. of pages
15
ISSN
0233-1934
Publication date
2024
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Control and Optimization, Management Science and Operations Research, Applied Mathematics
Electronic version(s)
https://doi.org/10.1080/02331934.2023.2256750 (Access: Closed)