Lagrange optimality system for a class of nonsmooth convex optimization

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms. We apply a linear Newton method to the Lagrange optimality system to obtain a novel algorithm applicable to a variety of nonsmooth convex optimization problems arising in practical applications. Under suitable conditions, we prove the nonsingularity of the Newton system and the local convergence of the algorithm.Comment: 19 page

Numerical homogenization of dual-phase steel by nonlinear conjugate gradient method (Recent developments on inverse problems for partial differential equations and their applications)

A numerical method is proposed to solve a cell problem for numerical homogenization of composite material, all of whose phases are homogeneous isotropic and whose deformations follow the elastoplastic constitutive law of Hencky's total strain theory

Identification of a mammalian vesicular polyamine transporter

Spermine and spermidine act as neuromodulators upon binding to the extracellular site(s) of various ionotropic receptors, such as N-methyl-d-aspartate receptors. To gain access to the receptors, polyamines synthesized in neurons and astrocytes are stored in secretory vesicles and released upon depolarization. Although vesicular storage is mediated in an ATP-dependent, reserpine-sensitive fashion, the transporter responsible for this process remains unknown. SLC18B1 is the fourth member of the SLC18 transporter family, which includes vesicular monoamine transporters and vesicular acetylcholine transporter. Proteoliposomes containing purified human SLC18B1 protein actively transport spermine and spermidine by exchange of H+. SLC18B1 protein is predominantly expressed in the hippocampus and is associated with vesicles in astrocytes. SLC18B1 gene knockdown decreased both SLC18B1 protein and spermine/spermidine contents in astrocytes. These results indicated that SLC18B1 encodes a vesicular polyamine transporter (VPAT)

CIP methods for hyperbolic system with variable and discontinuous coefficient

We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its derivative as unknowns and cubic Hermite interpolation for each computational cell. The exact update formula for solution and its derivative is derived and used for an efficient time integration. At points of discontinuity of wave speed we define a piecewise cubic Hermite interpolation based on immersed interface method. The method is extended to the one-dimensional Maxwell's equations with variable material properties.Comment: 19 page

The effects of co-medications on lamotrigine clearance in Japanese children with epilepsy

名古屋大学Nagoya University博士(医学)doctoral thesi