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Optimality Conditions and Gradient Descent Newton Pursuit for 0/1-Loss and Sparsity Constrained Optimization

Author

Listed:
  • Dongrui Wang

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China)

  • Hui Zhang

    (School of Management Science, Qufu Normal University, Rizhao Shandong 276800, P. R. China)

  • Penghe Zhang

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China)

  • Naihua Xiu

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, P. R. China)

Abstract

In this paper, we consider the optimization problems with 0/1-loss and sparsity constraints (0/1-LSCO) that involve two blocks of variables. First, we define a Ï„-stationary point of 0/1-LSCO, according to which we analyze the first-order necessary and sufficient optimality conditions. Based on these results, we then develop a gradient descent Newton pursuit algorithm (GDNP), and analyze its global and locally quadratic convergence under standard assumptions. Finally, numerical experiments on 1-bit compressed sensing demonstrate its superior performance in terms of a high degree of accuracy.

Suggested Citation

  • Dongrui Wang & Hui Zhang & Penghe Zhang & Naihua Xiu, 2024. "Optimality Conditions and Gradient Descent Newton Pursuit for 0/1-Loss and Sparsity Constrained Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 41(05), pages 1-34, October.
    • Handle: RePEc:wsi:apjorx:v:41:y:2024:i:05:n:s0217595923500355
    DOI: 10.1142/S0217595923500355
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