{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T17:04:43Z","timestamp":1776877483497,"version":"3.51.2"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,16]],"date-time":"2023-01-16T00:00:00Z","timestamp":1673827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["075-15-2022-1121"],"award-info":[{"award-number":["075-15-2022-1121"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Mor\u00e9 performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods.<\/jats:p>","DOI":"10.3390\/sym15010250","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T02:10:32Z","timestamp":1673921432000},"page":"250","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Improvement of Unconstrained Optimization Methods Based on Symmetry Involved in Neutrosophy"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0655-3741","authenticated-orcid":false,"given":"Predrag S.","family":"Stanimirovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia"},{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk 660041, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9179-0965","authenticated-orcid":false,"given":"Branislav","family":"Ivanov","sequence":"additional","affiliation":[{"name":"Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210 Bor, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6846-3074","authenticated-orcid":false,"given":"Dragi\u0161a","family":"Stanujki\u0107","sequence":"additional","affiliation":[{"name":"Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210 Bor, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8208-9656","authenticated-orcid":false,"given":"Vasilios N.","family":"Katsikis","sequence":"additional","affiliation":[{"name":"Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8299-9916","authenticated-orcid":false,"given":"Spyridon D.","family":"Mourtas","sequence":"additional","affiliation":[{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk 660041, Russia"},{"name":"Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-4001","authenticated-orcid":false,"given":"Lev A.","family":"Kazakovtsev","sequence":"additional","affiliation":[{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Prosp. Svobodny 79, Krasnoyarsk 660041, Russia"},{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, Prosp. Krasnoyarskiy Rabochiy 31, Krasnoyarsk 660037, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9349-5695","authenticated-orcid":false,"given":"Seyyed Ahmad","family":"Edalatpanah","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon P.O. Box 46818-53617, Mazandaran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,16]]},"reference":[{"key":"ref_1","unstructured":"Sun, W., and Yuan, Y.-X. (2006). Optimization Theory and Methods: Nonlinear Programming, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1023\/A:1025551602679","article-title":"A classification of quasi-Newton methods","volume":"33","author":"Brezinski","year":"2003","journal-title":"Numer. 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