Smoothing gradient descent algorithm for the composite sparse optimization

Smoothing Descent (aeronautics) Optimization algorithm
DOI: 10.3934/math.20241594 Publication Date: 2024-11-25T10:38:52Z
ABSTRACT
<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>
SUPPLEMENTAL MATERIAL
Coming soon ....
REFERENCES (43)
CITATIONS (0)
EXTERNAL LINKS
PlumX Metrics
RECOMMENDATIONS
FAIR ASSESSMENT
Coming soon ....
JUPYTER LAB
Coming soon ....