Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/67351
Title: | An augmented lagrangian method for non-Lipschitz nonconvex programming | Authors: | Chen, X Guo, L Lu, Z Ye, JJ |
Issue Date: | 2017 | Source: | SIAM journal on numerical analysis, 2017, v. 55, no. 1, p. 168-193 | Abstract: | We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration, and signal processing can be modelled in this form. First, we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz problem and show that it is necessary for optimality under a constraint qualification called the relaxed constant positive linear dependence (RCPLD) condition, which is weaker than the Mangasarian-Fromovitz constraint qualification and holds automatically if all the constraint functions are affine. Then we propose an augmented Lagrangian (AL) method in which the augmented Lagrangian subproblems are solved by a nonmonotone proximal gradient method. Under the assumption that a feasible point is known, we show that any accumulation point of the sequence generated by our method must be a feasible point. Moreover, if RCPLD holds at such an accumulation point, then it is a KKT point of the original problem. Finally, we conduct numerical experiments to compare the performance of our AL method and the interior point (IP) method for solving two sparse portfolio selection models. The numerical results demonstrate that our method is not only comparable to the IP method in terms of solution quality, but also substantially faster than the IP method. | Keywords: | Non-Lipschitz programming Sparse optimization Augmented Lagrangian method |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on numerical analysis | ISSN: | 0036-1429 | EISSN: | 1095-7170 | DOI: | 10.1137/15M1052834 | Rights: | © 2017 Society for Industrial and Applied Mathematics The following publication Chen, X., Guo, L., Lu, Z., & Ye, J. J. (2017). An augmented Lagrangian method for non-Lipschitz nonconvex programming. SIAM Journal on Numerical Analysis, 55(1), 168-193 is available at https://doi.org/10.1137/15M1052834 |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
15m1052834.pdf | 325.61 kB | Adobe PDF | View/Open |
Page views
207
Last Week
0
0
Last month
Citations as of Apr 14, 2024
Downloads
72
Citations as of Apr 14, 2024
SCOPUSTM
Citations
25
Last Week
0
0
Last month
Citations as of Apr 12, 2024
WEB OF SCIENCETM
Citations
27
Last Week
0
0
Last month
Citations as of Apr 18, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.