NDLI: Exact Penalty Decomposition Method for Zero-Norm Minimization Based on MPEC Formulation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bi, Shujun Pan, Shaohua Liu, Xiaolan
Copyright Year	2014
Abstract	We reformulate the zero-norm minimization problem as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Then, by the special structure of the exact penalty problem, we propose a decomposition method that can seek a global optimal solution of the zero-norm minimization problem under the null space condition in [M. A. Khajehnejad et al. IEEE Trans. Signal. Process., 59 (2011), pp. 1985--2001] by solving a finite number of weighted $l_1$-norm minimization problems. To handle the weighted $l_1$-norm subproblems, we develop a partial proximal point algorithm where the subproblems may be solved approximately with the limited memory BFGS (L-BFGS) or the semismooth Newton-CG. Finally, we apply the exact penalty decomposition method with the weighted $l_1$-norm subproblems solved by combining the L-BFGS with the semismooth Newton-CG to several types of sparse optimization problems, and compare its performance with that of the penalty decomposition method [Z. Lu and Y. Zhang, SIAM J. Optim., 23 (2013), pp. 2448--2478], the iterative support detection method [Y. L. Wang and W. T. Yin, SIAM J. Sci. Comput., 3 (2010), pp. 462--491], and the state-of-the-art code ${\bf FPC\_AS}$ [Z. W. Wen et al., SIAM J. Sci. Comput., 32 (2010), pp. 1832--1857]. Numerical comparisons indicate that the proposed method is very efficient in terms of the recoverability and the required computing time.
Starting Page	A1451
Ending Page	A1477
Page Count	27
File Format	PDF
ISSN	10648275
DOI	10.1137/110855867
e-ISSN	10957197
Issue Number	4
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-07-16
Access Restriction	Subscribed
Subject Keyword	MPECs decomposition method exact penalty Mathematical programming methods Nonconvex programming, global optimization zero-norm minimization Complementarity and equilibrium problems and variational inequalities
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in