Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/74150
PIRA download icon_1.1View/Download Full Text
Title: Optimality and complexity for constrained optimization problems with nonconvex regularization
Authors: Bian, W
Chen, X 
Issue Date: Nov-2017
Source: Mathematics of operations research, Nov. 2017, v. 42, no. 4, p. 1063-1084
Abstract: In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set, and the objective function has a nonsmooth, nonconvex regularizer. Such a regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding, and non-Lipschitz Lp penalties as special cases. Using the theory of the generalized directional derivative and the tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define the generalized stationary point of it. We show that the generalized stationary point is the Clarke stationary point when the objective function is Lipschitz continuous at this point, and satisfies the existing necessary optimality conditions when the objective function is not Lipschitz continuous at this point. Moreover, we prove the consistency between the generalized directional derivative and the limit of the classic directional derivatives associated with the smoothing function. Finally, we establish a lower bound property for every local minimizer and show that finding a global minimizer is strongly NP-hard when the objective function has a concave regularizer.
Keywords: Constrained nonsmooth nonconvex optimization
Directional derivative consistency
Generalized directional derivative
Numerical property
Optimality condition
Publisher: Institute for Operations Research and the Management Sciences
Journal: Mathematics of operations research 
ISSN: 0364-765X
EISSN: 1526-5471
DOI: 10.1287/moor.2016.0837
Rights: Copyright © 2017, INFORMS
This is the accepted manuscript of the following article: Bian, W., & Chen, X. (2017). Optimality and complexity for constrained optimization problems with nonconvex regularization. Mathematics of Operations Research, 42(4), 1063-1084, which has been published in final form at https://doi.org/10.1287/moor.2016.0837
Appears in Collections:Journal/Magazine Article

Files in This Item:
File Description SizeFormat 
Chen_Optimality_Complexity_For.pdfPre-Published version1.05 MBAdobe PDFView/Open
Open Access Information
Status open access
File Version Final Accepted Manuscript
Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page views

69
Citations as of Oct 2, 2022

Downloads

4
Citations as of Oct 2, 2022

SCOPUSTM   
Citations

16
Last Week
0
Last month
Citations as of Oct 6, 2022

WEB OF SCIENCETM
Citations

13
Last Week
0
Last month
Citations as of Oct 6, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.