ITM Web Conf.
Volume 36, 2021The 16th IMT-GT International Conference on Mathematics, Statistics and their Applications (ICMSA 2020)
|Number of page(s)||10|
|Section||Operations Research/Applied Mathematics|
|Published online||26 January 2021|
Spectral proximal method for solving large scale sparse optimization
Mathematical and Actuarial Sciences Department, Lee Kong Chian Faculty of Engineering and Science, University Tunku Abdul Rahman, 43000 Selangor, Malaysia
2 Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia
* Corresponding author: firstname.lastname@example.org
In this paper, we propose to use spectral proximal method to solve sparse optimization problems. Sparse optimization refers to an optimization problem involving the ι0 -norm in objective or constraints. The previous research showed that the spectral gradient method is outperformed the other standard unconstrained optimization methods. This is due to spectral gradient method replaced the full rank matrix by a diagonal matrix and the memory decreased from Ο(n2) to Ο(n). Since ι0-norm term is nonconvex and non-smooth, it cannot be solved by standard optimization algorithm. We will solve the ι0 -norm problem with an underdetermined system as its constraint will be considered. Using Lagrange method, this problem is transformed into an unconstrained optimization problem. A new method called spectral proximal method is proposed, which is a combination of proximal method and spectral gradient method. The spectral proximal method is then applied to the ι0-norm unconstrained optimization problem. The programming code will be written in Python to compare the efficiency of the proposed method with some existing methods. The benchmarks of the comparison are based on number of iterations, number of functions call and the computational time. Theoretically, the proposed method requires less storage and less computational time.
© The Authors, published by EDP Sciences, 2021
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