Details
| Original language | English |
|---|---|
| Pages (from-to) | 3323-3337 |
| Number of pages | 15 |
| Journal | OPTIMIZATION |
| Volume | 73 |
| Issue number | 11 |
| Early online date | 11 Sept 2023 |
| Publication status | Published - 2024 |
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.
Keywords
- coercive function, Dinkelbach type algorithm, Fractional optimization, partial minimizer
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Decision Sciences(all)
- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics
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In: OPTIMIZATION, Vol. 73, No. 11, 2024, p. 3323-3337.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Componentwise Dinkelbach algorithm for nonlinear fractional optimization problems
AU - Günther, Christian
AU - Orzan, Alexandru
AU - Precup, Radu
N1 - Publisher Copyright: © 2023 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - coercive function
KW - Dinkelbach type algorithm
KW - Fractional optimization
KW - partial minimizer
UR - http://www.scopus.com/inward/record.url?scp=85170687202&partnerID=8YFLogxK
U2 - 10.1080/02331934.2023.2256750
DO - 10.1080/02331934.2023.2256750
M3 - Article
AN - SCOPUS:85170687202
VL - 73
SP - 3323
EP - 3337
JO - OPTIMIZATION
JF - OPTIMIZATION
SN - 0233-1934
IS - 11
ER -