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LAGRANGIAN-DUAL FUNCTIONS AND MOREAU--YOSIDA REGULARIZATION.
- Source :
-
SIAM Journal on Optimization . 2008, Vol. 19 Issue 1, p39-61. 23p. - Publication Year :
- 2008
-
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 ? of the function φ, e.g., the semismoothness of the gradient g of the regularized function ?. 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 19
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 30095143
- Full Text :
- https://doi.org/10.1137/060673746