Dinkelbach Type Approximation Algorithms for Nonlinear Fractional Optimization Problems


In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland’s variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm.


Alexandru Orzan
Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania;
Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

Radu Precup
Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babes–Bolyai University, Cluj-Napoca, Romania;
Tiberiu Popoviciu Institute ofNumerical Analysis, Romanian Academy, Cluj-Napoca, Romania


Dinkelbach algorithm; Ekeland principle; fractional optimization; Palais-Smale condition.

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A. Orzan, R. Precup, Dinkelbach type approximation algorithms for nonlinear fractional optimization problems, Numerical Functional Analysis and Optimization, 44 (2023) no. 9, pp. 954–969. https://doi.org/10.1080/01630563.2023.2217893


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Numerical Functional Analysis and Optimization

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Taylor and Francis Ltd.

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