A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
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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.
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Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization
A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
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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.