Please use this identifier to cite or link to this item: https://doi.org/10.1137/060673746
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dc.titleLagrangian-dual functions and Moreau-Yosida regularization
dc.contributor.authorMeng, F.
dc.contributor.authorZhao, G.
dc.contributor.authorGoh, M.
dc.contributor.authorDe Souza, R.
dc.date.accessioned2013-10-09T06:18:05Z
dc.date.available2013-10-09T06:18:05Z
dc.date.issued2008
dc.identifier.citationMeng, 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
dc.identifier.issn10526234
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/44185
dc.description.abstractIn 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.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1137/060673746
dc.sourceScopus
dc.subjectFenchel conjugate
dc.subjectLagrangian dual
dc.subjectMoreau-Yosida regularization
dc.subjectPiecewise Ck functions
dc.subjectSemi-smoothness
dc.typeArticle
dc.contributor.departmentDECISION SCIENCES
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1137/060673746
dc.description.sourcetitleSIAM Journal on Optimization
dc.description.volume19
dc.description.issue1
dc.description.page39-61
dc.identifier.isiut000256708900003
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