The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem

Huan Gao (), Yingyi Li and Haibin Zhang ()
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Huan Gao: College of Mathematics and Computational Science, Hunan First Normal University, Changsha, Hunan 410205, P. R. China
Yingyi Li: Department of Basic Courses, Hebei Finance University, Baoding, Hebei 071051, P. R. China
Haibin Zhang: College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2020, vol. 37, issue 04, 1-16

Abstract: 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.

Keywords: Alternating minimization; double sparsity constrained problem; smooth function; convergence rate; partial gradient mappings (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0217595920400023

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