A New Forward–Backward Algorithm with Line Searchand Inertial Techniques for Convex Minimization Problems with Applications

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: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suthep Suantai: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2021, vol. 9, issue 13, 1-20

Abstract: For the past few decades, various algorithms have been proposed to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. The convergence of these algorithms was guaranteed under the L-Lipschitz condition on the gradient of the objective function. In recent years, an inertial technique has been widely used to accelerate the convergence behavior of an algorithm. In this work, we introduce a new forward–backward splitting algorithm using a new line search and inertial technique to solve convex minimization problems in the form of the sum of two lower semicontinuous and convex functions. A weak convergence of our proposed method is established without assuming the L-Lipschitz continuity of the gradient of the objective function. Moreover, a complexity theorem is also given. As applications, we employed our algorithm to solve data classification and image restoration by conducting some experiments on these problems. The performance of our algorithm was evaluated using various evaluation tools. Furthermore, we compared its performance with other algorithms. Based on the experiments, we found that the proposed algorithm performed better than other algorithms mentioned in the literature.

Keywords: convex minimization problems; machine learning; forward–backward algorithm; line search; accelerated algorithm; data classification; image restoration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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