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Volume 10
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Article

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

by
Dawan Chumpungam
1,
Panitarn Sarnmeta
2 and
Suthep Suantai
1,3,*
1
Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
KOSEN-KMITL, Bangkok 10520, Thailand
3
Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(9), 1491; https://doi.org/10.3390/math10091491
Submission received: 16 March 2022 / Revised: 22 April 2022 / Accepted: 27 April 2022 / Published: 30 April 2022
(This article belongs to the Special Issue Advances in Machine Learning and Mathematical Modeling for Optimization Problems)
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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 forward–backward algorithm; line search; accelerated algorithm; convex minimization problems; data classification; machine learning

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MDPI and ACS Style

Chumpungam, D.; Sarnmeta, P.; Suantai, S. An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning. Mathematics 2022, 10, 1491. https://doi.org/10.3390/math10091491

AMA Style

Chumpungam D, Sarnmeta P, Suantai S. An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning. Mathematics. 2022; 10(9):1491. https://doi.org/10.3390/math10091491

Chicago/Turabian Style

Chumpungam, Dawan, Panitarn Sarnmeta, and Suthep Suantai. 2022. "An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning" Mathematics 10, no. 9: 1491. https://doi.org/10.3390/math10091491

APA Style

Chumpungam, D., Sarnmeta, P., & Suantai, S. (2022). An Accelerated Convex Optimization Algorithm with Line Search and Applications in Machine Learning. Mathematics, 10(9), 1491. https://doi.org/10.3390/math10091491

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