Proximal variable metric method with spectral diagonal update for large scale sparse optimization
We will tackle the l0-norm sparse optimization problem using an underdetermined system as a constraint in this research. This problem is turned into an unconstrained optimization problem using the Lagrangian method and solved using the proximal variable metric method. This approach combines the p...
| Main Authors: | , , , |
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| Format: | Article |
| Published: |
Elsevier
2023
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| Online Access: | http://psasir.upm.edu.my/id/eprint/109005/ |
| Summary: | We will tackle the l0-norm sparse optimization problem using an underdetermined system as a
constraint in this research. This problem is turned into an unconstrained optimization problem using
the Lagrangian method and solved using the proximal variable metric method. This approach combines
the proximal and variable metric methods by substituting a diagonal matrix for the approximation of
the full rank Hessian matrix. Hence, the memory requirement is reduced to O(n) storage instead of
O(n2 ) storage. The diagonal updating matrix is derived from the same variational technique used in
the derivation of variable metric or quasi-Newton updates but incorporated with some weaker form
of quasi-Newton relation. Convergence analysis of this method is established. The efficiency of the
proposed method is compared against existing versions of proximal gradient methods on simulated
datasets and large real-world MNIST datasets using Python software. Numerical results show that our
proposed method is more robust and stable for finding sparse solutions to the linear system. |
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