The optimized Schwarz method and the closely related 2-Lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations. Although these methods are known to work well in special cases (e.g., when the domain is a square and the two subdomains are rectangles), the problem has never been systematically stated nor analyzed f...

The alternating direction method of multipliers (ADMM) is an application of the Douglas-Rachford splitting method; and the symmetric version of ADMM which updates the Lagrange multiplier twice at each iteration is an application of the Peaceman-Rachford splitting method. Sometimes the symmetric ADMM works empirically; but theoretically its convergence is not guaranteed. It was recently found th...

In this paper we explain how to characterize the best approximation to any x in a Hilbert space X from the set C ∩ {x ∈ X : gi(x) ≤ 0, i = 1, 2, · · · ,m} in the face of data uncertainty in the convex constraints, gi(x) ≤ 0, i = 1, 2, · · · ,m, where C is a closed convex subset of X. Following the robust optimization approach, we establish Lagrange multiplier characterizations of the robust con...

Rate-distortion optimization (RDO) plays an essential role in substantially enhancing the coding efficiency. Currently, rate-distortion optimized mode decision is widely used in scalable video coding (SVC). Among all the possible coding modes, it aims to select the one which has the best trade-off between bitrate and compression distortion. Specifically, this tradeoff is tuned through the choic...

The use of regression-based specification tests, such as the nR2 form of the Lagrange Multiplier test, has become quite widespread over the last 20 years. The popularization of the nR2 form of the Lagrange Multiplier (LM) test, perhaps the most widely used class of regression-based tests, has come about in large part from the ease of its application to many tests of nonlinear restrictions and i...

The study of fractional variational problems with derivatives in the sense of Caputo is a recent subject, the main results being Agrawal’s necessary optimality conditions of Euler-Lagrange and respective transversality conditions. Using Agrawal’s Euler-Lagrange equation and the Lagrange multiplier technique, we obtain here a Noether-like theorem for fractional optimal control problems in the se...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

in this paper, we consider the variational homotopy perturbation method (vhpm) to obtain an approximate series solution for the generalized fisher’s equation which converges to the exact solution in the region of convergence. comparisons are made among the variational iteration method (vim), the exact solutions and the proposed method. the results reveal that the proposed method is very effectiv...