{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:38:32Z","timestamp":1760236712816,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T00:00:00Z","timestamp":1639958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.<\/jats:p>","DOI":"10.3390\/sym13122450","type":"journal-article","created":{"date-parts":[[2021,12,20]],"date-time":"2021-12-20T02:40:32Z","timestamp":1639968032000},"page":"2450","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration"],"prefix":"10.3390","volume":"13","author":[{"given":"Jun","family":"Huo","sequence":"first","affiliation":[{"name":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530003, China"}]},{"given":"Yuping","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Guangxi University, Nanning 530005, China"}]},{"given":"Guoen","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Business Administration, Guangxi University of Finance and Economics, Nanning 530003, China"}]},{"given":"Shengwei","family":"Yao","sequence":"additional","affiliation":[{"name":"Guangxi (ASEAN) Financial Research Center, Guangxi University of Finance and Economics, Nanning 530003, China"},{"name":"Guangxi Key Laboratory Cultivation Base of Cross-Border E-Commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning 530003, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/0041-5553(69)90035-4","article-title":"The conjugate gradient method in extreme problems","volume":"9","author":"Polyak","year":"1969","journal-title":"USSR Comput. 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