{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T03:07:19Z","timestamp":1648782439636},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:p> This work analyzes the alternating minimization (AM) method for solving double sparsity constrained minimization problem, where the decision variable vector is split into two blocks. The objective function is a separable smooth function in terms of the two blocks. We analyze the convergence of the method for the non-convex objective function and prove a rate of convergence of the norms of the partial gradient mappings. Then, we establish a non-asymptotic sub-linear rate of convergence under the assumption of convexity and the Lipschitz continuity of the gradient of the objective function. To solve the sub-problems of the AM method, we adopt the so-called iterative thresholding method and study their analytical properties. Finally, some future works are discussed. <\/jats:p>","DOI":"10.1142\/s0217595920400023","type":"journal-article","created":{"date-parts":[[2020,5,19]],"date-time":"2020-05-19T05:37:52Z","timestamp":1589866672000},"page":"2040002","source":"Crossref","is-referenced-by-count":1,"title":["The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem"],"prefix":"10.1142","volume":"37","author":[{"given":"Huan","family":"Gao","sequence":"first","affiliation":[{"name":"College of Mathematics and Computational Science, Hunan First Normal University, Changsha, Hunan 410205, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingyi","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Basic Courses, Hebei Finance University, Baoding, Hebei 071051, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haibin","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. 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