Smoothing gradient descent algorithm for the composite sparse optimization

• DOI: 10.3934/math.20241594
• Publication Date: 2024-11-25T10:38:52Z
• Authors: Wei Yang; Lili Pan; Jinhui Wan
• Keywords: Smoothing; Descent (aeronautics); Optimization algorithm

<p>Composite sparsity generalizes the standard that considers on a linear transformation of variables. In this paper, we study composite sparse optimization problem consisting minimizing sum nondifferentiable loss function and $ {\mathcal{\ell}_0} penalty term matrix times coefficient vector. First, consider an exact continuous relaxation with capped-$ {\mathcal{\ell}_1} has same optimal solution as primal problem. Specifically, propose lifted stationary point then establish equivalence original problems. Second, smoothing gradient descent (SGD) algorithm for problem, which solves subproblem inexactly since objective is inseparable. We show if sequence generated by SGD accumulation point, it point. At last, present several computational examples to illustrate efficiency algorithm.</p>