A New Accelerated Algorithm Based on Fixed Point Method for Convex Bilevel Optimization Problems with Applications

Piti Thongsri, Bancha Panyanak and Suthep Suantai ()
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Piti Thongsri: PhD Degree Program in Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Bancha Panyanak: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suthep Suantai: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: A new accelerated common fixed point algorithm is introduced and analyzed for a countable family of nonexpansive mappings and then we apply it to solve some convex bilevel optimization problems. Then, under some suitable conditions, we prove a strong convergence result of the proposed algorithm. As an application, we employ the proposed algorithm for regression and classification problems. Moreover, we compare the performance of our algorithm with others. By numerical experiments, we found that our algorithm has a better performance than the others.

Keywords: bilevel optimization; fixed point algorithm; forward-backward algorithm; regression and classification problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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