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Compared to traditional methods for solving such equations, this method utilizes three\u2010step successive information to produce inertial iterates. The proposed composite search direction framework incorporates an effective restart strategy, eliminating the need for additional conditions, including the specification of conjugate parameter, and satisfies conditions for the sufficient descent condition and trust region property. Establishing the theoretical convergence of the present method does not require Lipschitz continuity. Furthermore, we analyze the asymptotic and non\u2010asymptotic convergence rates in terms of iteration complexity. To evaluate effectiveness, comparative tests are conducted against existing methods using problems related to the system of nonlinear equations. Moreover, the practicality of the presented method is demonstrated through applications in compressed sensing.<\/jats:p>","DOI":"10.1002\/nla.70035","type":"journal-article","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T06:22:43Z","timestamp":1758867763000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Accelerated Spectral CG\u2010Type Projection Method With Restart Strategy for Nonlinear Monotone Equations and Applications in Compressed Sensing"],"prefix":"10.1002","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9176-6321","authenticated-orcid":false,"given":"Pengjie","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics China University of Mining and Technology  Xuzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linhao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics China University of Mining and Technology  Xuzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7816-0707","authenticated-orcid":false,"given":"Hu","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Mathematics China University of Mining and Technology  Xuzhou China"},{"name":"Jiangsu Center for Applied Mathematics (CUMT) China University of Mining and Technology  Xuzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bowen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Statistics University of Oxford  Oxford UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,9,25]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2021.3056567"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-022-02135-3"},{"issue":"4","key":"e_1_2_9_4_1","first-page":"457","article-title":"A Spectral Gradient Projection Algorithm for Convex Constrained Nonsmooth Equations Based on an Adaptive Line Search","volume":"42","author":"Yin J. 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