Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10898-008-9333-7
Title: Moreau-Yosida regularization of Lagrangian-dual functions for a class of convex optimization problems
Authors: Meng, F. 
Keywords: Lagrangian dual
Moreau-Yosida regularization
Piecewise C k functions
Semismoothness
Issue Date: Jul-2009
Citation: Meng, F. (2009-07). Moreau-Yosida regularization of Lagrangian-dual functions for a class of convex optimization problems. Journal of Global Optimization 44 (3) : 375-394. ScholarBank@NUS Repository. https://doi.org/10.1007/s10898-008-9333-7
Abstract: In this paper, we consider the Lagrangian dual problem of a class of convex optimization problems, which originates from multi-stage stochastic convex nonlinear programs. We study the Moreau-Yosida regularization of the Lagrangian-dual function and prove that the regularized function η is piecewise C 2, in addition to the known smoothness property. This property is then used to investigate the semismoothness of the gradient mapping of the regularized function. Finally, we show that the Clarke generalized Jacobian of the gradient mapping is BD-regular under some conditions. © 2008 Springer Science+Business Media, LLC.
Source Title: Journal of Global Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/115816
ISSN: 09255001
DOI: 10.1007/s10898-008-9333-7
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