A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Piecewise smoothness, local invertibility, and parametric analysis of normal maps
Mathematics of Operations Research
Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
SIAM Journal on Numerical Analysis
A Globally and Superlinearly Convergent Algorithm for Nonsmooth Convex Minimization
SIAM Journal on Optimization
Semismooth Matrix-Valued Functions
Mathematics of Operations Research
Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Mathematics of Operations Research
A Lagrangian Dual Method with Self-Concordant Barriers for Multi-Stage Stochastic Convex Programming
Mathematical Programming: Series A and B
Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
Mathematical Programming: Series A and B
Lagrangian-Dual Functions and Moreau-Yosida Regularization
SIAM Journal on Optimization
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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 驴 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.