Proximal Gradient Method for Solving Bilevel Optimization Problems

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly converge...

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Bibliographic Details
Published inMathematical and computational applications Vol. 25; no. 4; p. 66
Main Authors Yimer, Seifu Endris, Kumam, Poom, Gebrie, Anteneh Getachew
Format Journal Article
LanguageEnglish
Published MDPI AG 04.10.2020
Subjects
bilevel problem
fixed point problem
gradient method
proximal method
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Summary:In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.
ISSN:2297-8747
1300-686X
2297-8747
DOI:10.3390/mca25040066