{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T11:54:39Z","timestamp":1764158079469,"version":"3.46.0"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T00:00:00Z","timestamp":1764115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this study, we introduce two efficient derivative-free algorithms enhanced by a restart strategy to solve nonlinear pseudomonotone equations. We demonstrate that the algorithm\u2019s search direction is both descent and bounded, and under the assumptions of pseudomonotonicity and continuity, the algorithm generates globally convergent sequences toward the solutions. Numerical experiments on benchmark test problems highlight the computational efficiency of our proposed algorithm compared to several existing methods. Additionally, we illustrate the algorithm\u2019s applicability to logistic regression problems, showcasing its practical relevance.<\/jats:p>","DOI":"10.3390\/a18120743","type":"journal-article","created":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T11:43:22Z","timestamp":1764157402000},"page":"743","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two Classes of Restart Algorithms for Solving Pseudomonotone Nonlinear Equations"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9797-2022","authenticated-orcid":false,"given":"Jitsupa","family":"Deepho","sequence":"first","affiliation":[{"name":"Faculty of Science, Energy and Environment, King Mongkut\u2019s University of Technology North Bangkok, 19 Moo 11, Tambon Nonglalok, Amphur Bankhai, Rayong 21120, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6142-3694","authenticated-orcid":false,"given":"Auwal Bala","family":"Abubakar","sequence":"additional","affiliation":[{"name":"Department of Art and Science, George Mason University, Songdomunhwa-ro 119-4, Yeonsu-gu, Incheon 21985, Republic of Korea"},{"name":"Numerical Optimization Research Group, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano 700241, Nigeria"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, Medunsa, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5534-1759","authenticated-orcid":false,"given":"Abdulkarim Hassan","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Data Science, Emirates Aviation University, Dubai 53044, United Arab Emirates"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria 0204, Medunsa, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s40314-020-01151-5","article-title":"A note on the spectral gradient projection method for nonlinear monotone equations with applications","volume":"39","author":"Abubakar","year":"2020","journal-title":"Comput. 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