This paper provides for the first time some computable smoothing functions for variational inequality problems with general constraints. This paper proposes also a new version of the smoothing Newton method and establishes its global and superlinear (quadratic) convergence under conditions weaker than those previously used in the literature. These are achieved by introducing a general definitio...

Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is appli...

The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems, can be regarded as a variant of the smoothing method. At the kth step, the nonsmooth function F is approximated by a smooth function f(·, εk), and the derivative of f(·, εk) at xk is used as the Newto...

The smoothing procedure has been introduced by Schh onauer as an acceleration algorithm for the Generalized Conjugate Gradient methods. In this paper, after giving our deenition of Conjugate Gradient type methods, and using a Generalized Hessenberg process, we introduce a Hybrid generalized Conjugate Gradient type method. We show that this Hybrid procedure is a variable smoothing procedure. And...

In Gardner (1985), I reviewed the research in exponential smoothing since the original work by Brown and Holt. This paper brings the state of the art up to date. The most important theoretical advance is the invention of a complete statistical rationale for exponential smoothing based on a new class of state-space models with a single source of error. The most important practical advance is the...