{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T16:48:42Z","timestamp":1789750122216,"version":"4.0.1"},"reference-count":28,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,4]],"date-time":"2020-08-04T00:00:00Z","timestamp":1596499200000},"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 paper, we propose a new version of the generalized damped Gauss\u2013Newton method for solving nonlinear complementarity problems based on the transformation to the nonsmooth equation, which is equivalent to some unconstrained optimization problem. The B-differential plays the role of the derivative. We present two types of algorithms (usual and inexact), which have superlinear and global convergence for semismooth cases. These results can be applied to efficiently find all solutions of the nonlinear complementarity problems under some mild assumptions. The results of the numerical tests are attached as a complement of the theoretical considerations.<\/jats:p>","DOI":"10.3390\/a13080190","type":"journal-article","created":{"date-parts":[[2020,8,4]],"date-time":"2020-08-04T10:45:17Z","timestamp":1596537917000},"page":"190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On a Nonsmooth Gauss\u2013Newton Algorithms for Solving Nonlinear Complementarity Problems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6557-6436","authenticated-orcid":false,"given":"Marek J.","family":"\u015amieta\u0144ski","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 \u0141\u00f3d\u017a, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/0131009","article-title":"Equivalence of the complementarity problem to a system of nonlinear equations","volume":"31","author":"Mangasarian","year":"1976","journal-title":"SIAM J. 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