A smoothing projected gradient (SPG) method is proposed for the minimization problem on a closed convex set, where the objective function is locally Lipschitz continuous but nonconvex, nondifferentiable. We show that any accumulation point generated by the SPG method is a stationary point associated with the smoothing function used in the method, which is a Clarke stationary point in many appli...

Abstract Local regularization methods allow for the application of sequential solution techniques for the solution of Volterra problems, retaining the causal structure of the original Volterra problem and leading to fast solution techniques. Stability and convergence of these methods was shown to hold on a large class of linear Volterra problems, i.e., the class of ν-smoothing problems for ν = ...

We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditioned ...

We numerically analyze the possibility of turning off postsmoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditio...

We consider wavelet estimation of the time–dependent (evolutionary) power spectrum of a locally stationary time series. Hereby, wavelets are used to provide an adaptive local smoothing of a short–time periodogram in the time–frequency plane. For this, in contrast to classical nonparametric (linear) approaches we use non–linear thresholding of the empirical wavelet coefficients. We show how thes...

It is known that the fitted regression function based on conventional local smoothing procedures is not statistically consistent at jump positions of the true regression function. In this article, a curve-fitting procedure based on local piecewise-linear kernel estimation is suggested. In a neighborhood of a given point, a piecewise-linear function with a possible jump at the given point is fit...

Exponential procedures are widely used as forecasting techniques for inventory control and business planning. A number of modifications to the generalized exponential smoothing (Holt–Winters) approach to forecasting univariate time series is presented, which have been adapted into a tool for decision support systems. This methodology unifies the phases of estimation and model selection into jus...

For spline smoothing one can rewrite the smooth estimation as a linear mixed model (LMM) where the smoothing parameter appears as the variance of spline basis coefficients. Smoothing methods that use basis functions with penalization can utilize maximum likelihood (ML) theory in LMM framework ([8]). We introduce the minimum description length (MDL) model selection criterion in LMM and propose a...

Nonparametric profile monitoring (NPM) is for monitoring over time a functional relationship between a response variable and one or more explanatory variables when the relationship is too complicated to be specified parametrically. It is widely used in industry for the purpose of quality control of a process. Existing NPM approaches require a fundamental assumption that design points within a p...

This article uses local polynomial techniques to t Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary eeect is noted. We show that the Whittle likelihood based estimator has advantages over the least-squares based log-periodogram. The bandwidth for the Whittle likel...