{"title":"Computational performance of a generalized descent gradient method based algorithm with conformable fractional-order derivatives","authors":"Marcio Antônio de Andrade Bortoloti","doi":"10.1016/j.cam.2024.116480","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we perform an analysis of the Descent Gradient Method (DGM) within the context of the conformable fractional derivatives. We explore the mathematical properties of functions with continuous Lipschitz gradients. Notably, this fractional derivative approach significantly reduced computational effort when compared to the conventional DGM. Additionally, we present a detailed numerical example to prove the high performance of this generalized DGM algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116480"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724007283","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we perform an analysis of the Descent Gradient Method (DGM) within the context of the conformable fractional derivatives. We explore the mathematical properties of functions with continuous Lipschitz gradients. Notably, this fractional derivative approach significantly reduced computational effort when compared to the conventional DGM. Additionally, we present a detailed numerical example to prove the high performance of this generalized DGM algorithm.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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