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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Huan Gao & Yingyi Li & Haibin Zhang, 2020. "The Analysis of Alternating Minimization Method for Double Sparsity Constrained Optimization Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-16, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400023
    DOI: 10.1142/S0217595920400023
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