This paper is devoted to the approximation by a piecewise linear finite element method of a noncoercive system of elliptic quasi-variational inequalities arising in the management of energy production. A quasi-optimal L∞ error estimate is established, using the concept of subsolution.

We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing a trade-off between computation time and accuracy. We expand the variational approximating class by incorpor...

When using thresholding method to segment an image, a fixed threshold is not suitable if the background is uneven. Here, we propose a new adaptive thresholding method using variational theory. The method requires only one parameter to be selected and the adaptive threshold surface can be found automatically from the original image.

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...