Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 920-933.

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The Greedy Simplex Algorithm for Double Sparsity Constrained Optimization Problems

Tingwei Pan(),Suxiang He*()   

  1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070
  • Received:2021-07-05 Online:2022-06-26 Published:2022-05-09
  • Contact: Suxiang He;
  • Supported by:
    the NSFC(11871153)


In view of the shortcomings of the alternating minimization method in which it needs to calculate the Lipschitz constant of the objective function gradient and the Lipschitz condition is needed to construct the L-stable point of the problem, this paper proposes a greedy simplex algorithm to solve the optimization problems with double sparse constraints. The CW optimality condition for double sparse constrained optimization problems is described. Based on the CW optimality condition, the iterative steps of the algorithm are designed, and the global convergence of the sequence of iterative points generated by the algorithm to the optimal solution of the problem is proved under the weaker assumptions.

Key words: Dual sparse constrained optimization problems, CW optimality condition, Greedy simplex algorithm, Global convergence

CLC Number: 

  • O224