We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At ...

We propose a proximal Newton method for solving nondiieren-tiable convex optimization. This method combines the generalized Newton method with Rockafellar's proximal point algorithm. At each step, the proximal point is found approximately and the regu-larization matrix is preconditioned to overcome inexactness of this approximation. We show that such a preconditioning is possible within some ac...

The Miyadera perturbation theorem provides as a by-product that operators defined on a core for the generator of a C0-semigroup and satisfying the Miyadera condition have a relatively bounded extension to the domain of the generator. We show that a weakening of the Miyadera condition characterizes relative boundedness with respect to the generator. We also investigate extensions of these result...

This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (2016) when applied to log-concave probability distributions that are restricted to a convex body K. This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with K. Explicit convergence bounds i...

Relying on the Yosida approximate, we investigate the problem of finding zeroes for a difference of two maximal monotone operators in Hilbert spaces. These zeroes are compared to those of the corresponding regularized and dual problems. The behavior of the regularized operator is also studied and a splitting algorithm involving the resolvents of both operators is suggested via a fixed-point for...

In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...

We study the exchange coupling mediated by itinerant carriers with spin-orbit interaction by both analytic and numeric approaches. The mediated exchange coupling is noncollinear and its spatial trends depend on the Fermi-surface topology of the itinerant carriers. Taking Rashba interaction as an example, the exchange coupling is similar to the conventional Ruderman-Kittel-Kasuya-Yosida type in ...

We infer the magnitude of the superfluid gap for He in aerogel from measurements of the normal fluid density as a function of temperature. We compute the effective Yosida function for two different aerogel samples over a range of pressures. We find that the suppression factor of the zero-temperature superfluid gap, scaled by kBTc , ranges from 0.5 to 0.8 as compared to the pressure-dependent we...

We propose an iterative method that solves a nonsmooth convex optimization problem by converting the original objective function to a once continuously differentiable function by way of Moreau-Yosida regularization. The proposed method makes use of approximate function and gradient values of the MoreauYosida regularization instead of the corresponding exact values. Under this setting, Fukushima...