Please use this identifier to cite or link to this item: https://doi.org/10.1137/060673746
Title: Lagrangian-dual functions and Moreau-Yosida regularization
Authors: Meng, F.
Zhao, G. 
Goh, M. 
De Souza, R.
Keywords: Fenchel conjugate
Lagrangian dual
Moreau-Yosida regularization
Piecewise Ck functions
Semi-smoothness
Issue Date: 2008
Source: Meng, F., Zhao, G., Goh, M., De Souza, R. (2008). Lagrangian-dual functions and Moreau-Yosida regularization. SIAM Journal on Optimization 19 (1) : 39-61. ScholarBank@NUS Repository. https://doi.org/10.1137/060673746
Abstract: In this paper, we consider the Lagrangian-dual problem of a class of convex optimization problems. We first discuss the semismoothness of the Lagrangian-dual function φ. This property is then used to investigate the second-order properties of the Moreau-Yosida regularization η of the function φ, e.g., the semismoothness of the gradient g of the regularized function η. We show that φ and g are piecewise C2 and semismooth, respectively, for certain instances of the optimization problem. We establish a relationship between the original problem and the Fenchel conjugate of the regularization of the corresponding Lagrangian dual problem. We also find some instances of the optimization problem whose Lagrangian-dual function φ is not piecewise smooth. However, its regularized function still possesses nice second-order properties. Finally, we provide an alternative way to study the semismoothness of the gradient under the structure of the epigraph of the dual function. © 2008 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/44185
ISSN: 10526234
DOI: 10.1137/060673746
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
2008-lagrangian_dual_functions_moreau_yosida-published.pdf254.62 kBAdobe PDF

OPEN

PublishedView/Download

SCOPUSTM   
Citations

4
checked on Dec 6, 2017

WEB OF SCIENCETM
Citations

4
checked on Nov 21, 2017

Page view(s)

61
checked on Dec 10, 2017

Download(s)

11
checked on Dec 10, 2017

Google ScholarTM

Check

Altmetric


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