A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.
Toland,The dual of L∞(X,L, λ ), finitely additive measures and weak convergence
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A $\operatorname{prox}$-Based Semi-Smooth Newton Method for Convex Variational Problems
A prox-based semi-smooth Newton method is proposed for finite-element discretizations of convex variational problems, with global well-posedness and local superlinear convergence established under suitable assumptions on energy densities.