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

Dongrui Wang, Hui Zhang (), Penghe Zhang () and Naihua Xiu ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 05, 1-34

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.

Keywords: 0/1-loss and sparsity constrained optimization; optimality condition; gradient descent Newton pursuit; global convergence; locally quadratic convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500355

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