A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems

In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point set...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 12; no. 3; p. 377
Main Author Nimana, Nimit
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2020
Subjects
Algorithms
Convex analysis
Convexity
Fixed points (mathematics)
Inverse problems
Linear transformations
Operators (mathematics)
Optimization
Splitting
Wavelet transforms
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Summary:In this work, we consider a bilevel optimization problem consisting of the minimizing sum of two convex functions in which one of them is a composition of a convex function and a nonzero linear transformation subject to the set of all feasible points represented in the form of common fixed-point sets of nonlinear operators. To find an optimal solution to the problem, we present a fixed-point subgradient splitting method and analyze convergence properties of the proposed method provided that some additional assumptions are imposed. We investigate the solving of some well known problems by using the proposed method. Finally, we present some numerical experiments for showing the effectiveness of the obtained theoretical result.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym12030377