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...

In this paper we report on the design and analysis of a multilevel method for the solution of the OrnsteinZernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson-Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method.

We consider the linear quadratic differential games for positive linear systems with the feedback information structure and two players. The Newton method to obtain the stabilizing solution of a corresponding set of Riccati equations is presented in the literature. Here, we modify the Newton method and propose a new faster iterative method. Moreover, the convergence properties of the modificati...

We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel...

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...

The notion of Newton–like inequalities is extended and an inductive approach is utilized to show that the generalized Newton–like inequalities hold on elementary symmetric functions with self–conjugate variables in the right half–plane.

In this paper, a local minimax-Newton method is developed to solve for multiple saddle points. The local minimax method [15] is used to locate an initial guess and a version of the generalized Newton method is used to speed up convergence. When a problem possesses a symmetry, the local minimax method is invariant to the symmetry. Thus the symmetry can be used to greatly enhance the efficiency a...

We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random varia...

This paper is devoted to the study of the proximal point algorithm for solving monotone and nonmonotone nonlinear complementarity problems. The proximal point algorithm is to generate a sequence by solving subproblems that are regularizations of the original problem. After given an appropriate criterion for approximate solutions of subproblems by adopting a merit function, the proximal point al...

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of the following of the reduced gradient (RGF) [see Quapp et al., Theoret. Chem. Acc. 100 (1998) 285], also named the Newton trajectory. All the important features of the potential energy surface are definable independently of the coordinate system. We demonstrate it for the Newton trajec...