{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T04:06:46Z","timestamp":1769314006053,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T00:00:00Z","timestamp":1657152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Taif University Researches Supporting Project","award":["TURSP-2020\/326"],"award-info":[{"award-number":["TURSP-2020\/326"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we propose two scaled Dai\u2013Yuan (DY) directions for solving constrained monotone nonlinear systems. The proposed directions satisfy the sufficient descent condition independent of the line search strategy. We also reasonably proposed two different relations for computing the scaling parameter at every iteration. The first relation is proposed by approaching the quasi-Newton direction, and the second one is by taking the advantage of the popular Barzilai\u2013Borwein strategy. Moreover, we propose a robust projection-based algorithm for solving constrained monotone nonlinear equations with applications in signal restoration problems and reconstructing the blurred images. The global convergence of this algorithm is also provided, using some mild assumptions. Finally, a comprehensive numerical comparison with the relevant algorithms shows that the proposed algorithm is efficient.<\/jats:p>","DOI":"10.3390\/sym14071401","type":"journal-article","created":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T22:11:47Z","timestamp":1657231907000},"page":"1401","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Scaled Dai\u2013Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6076-625X","authenticated-orcid":false,"given":"Ali","family":"Althobaiti","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, Taif University, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7262-490X","authenticated-orcid":false,"given":"Jamilu","family":"Sabi\u2019u","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Yusuf Maitama Sule University, Kano P.M.B. 3099, Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Homan","family":"Emadifar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 1584743311, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prem","family":"Junsawang","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4524-1951","authenticated-orcid":false,"given":"Soubhagya Kumar","family":"Sahoo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101174","DOI":"10.1016\/j.najef.2020.101174","article-title":"Efficient predictability of stock return volatility: The role of stock market implied volatility","volume":"52","author":"Dai","year":"2020","journal-title":"N. 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