The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discretization of thin plate splines. The mixed formulation is obtained by introducing the gradient of the smoother as an additional unknown. Working with a pair of bases for the gradient of the smoother and the Lagrange m...

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadraticgrowth condition. We show that such programs can be transformed, by relaxing the constraints and adding a linear penalty term to the objective function, into equivalent nonlinear programs that have diierentiable data and a bounded Lagrange multiplier set and that s...

We investigate nonlinear programs that have a nonempty but possibly unbounded Lagrange multiplier set and that satisfy the quadratic growth condition. We show that such programs can be transformed, by relaxing the constraints and adding a linear penalty term to the objective function, into equivalent nonlinear programs that have differentiable data and a bounded Lagrange multiplier set and that...

Locally asymptotically most stringent tests for autoregressive against diagonal bilinear time series models are derived. A (restricted) local asymptotic normality property is therefore established for bilinear processes in the vicinity of linear autoregressive ones. The behaviour of the bispectrum under local alternatives of bilinear dependence shows the danger of misinterpreting skewness or ku...

The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration method-II (VIM). Through careful investigation of the earlier variational ...

We consider convex quadratic programs with large numbers of constraints. We distribute these constraints among several parallel processors and modify the objective function for each of these subproblems with Lagrange multiplier information from the other processors. New Lagrange multiplier information is aggregated in a master processor and the whole process is repeated. Linear convergence is e...

The Lagrange multiplier based rate−distortion optimization has been proved an effective technique in hybrid video codec design. To improve the coding efficiency, an efficient Lagrange multiplier selection method is presented in this paper. As an extension to our previous work, the Laplace distribution based rate model is further refined by taking correlations among successive frames into accoun...

It is demonstrated that the pre-dual for problems with total bounded variation regularization terms can be expressed as bilaterally constrained optimization problem. Existence of a Lagrange multiplier and an optimality system are established. This allows to utilize efficient optimization methods developed for problems with box constraints in the context of bounded variation formulations. Here, ...

The Lagrangian coder control together with the parameter choice is presented that lead to the creation of the new hybrid video coder specifications TMN-10 for H.263 and TML for H.26L. An efEcient approach for the determination of the encoding parameters is developed. It is shown by means of experimental results that the Lagrange multiplier for the macroblock mode decision corre sponds to the ne...

-Using the He’s variational iteration method, it is possible to find the exact solutions or better approximate solutions of the partial differential equations. In this method, a correction functional is constructed by a general Lagrange multiplier, which can be identified via variational theory. In this paper, this method is used for solving a nonlinear partial differential equation, a three-di...