An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning

Dawan Chumpungam, Panitarn Sarnmeta and Suthep Suantai
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Dawan Chumpungam: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Panitarn Sarnmeta: KOSEN-KMITL, Bangkok 10520, Thailand
Suthep Suantai: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2022, vol. 10, issue 9, 1-20

Abstract: In this paper, we introduce a new line search technique, then employ it to construct a novel accelerated forward–backward algorithm for solving convex minimization problems of the form of the summation of two convex functions in which one of these functions is smooth in a real Hilbert space. We establish a weak convergence to a solution of the proposed algorithm without the Lipschitz assumption on the gradient of the objective function. Furthermore, we analyze its performance by applying the proposed algorithm to solving classification problems on various data sets and compare with other line search algorithms. Based on the experiments, the proposed algorithm performs better than other line search algorithms.

Keywords: forward–backward algorithm; line search; accelerated algorithm; convex minimization problems; data classification; machine learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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