This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker ...

in this paper, he's highly prolic variational iteration method is applied ef-fectively for showing the existence, uniqueness and solving a class of singularsecond order two point boundary value problems. the process of nding solu-tion involves generation of a sequence of appropriate and approximate iterativesolution function equally likely to converge to the exact solution of the givenpr...

Abstract In this paper, we present a new simple method for solving two integral equations of Love’s type that have many applications, especially in electrostatic systems. The approach the solution is based on an innovative technique using matrix algebra barycentric Lagrange interpolation. unknown function expressed through product four matrices. kernel interpolated twice, so get it five Additio...

The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange formula is shown to be backward stable. The barycentric formula has a less favourable error analysis, bu...

A constrained optimization method, called the Lagrange-Hoppeld (LH) method, is presented for solving Markov random eld (MRF) based Bayesian image estimation problems for restoration and segmentation. The method combines the augmented Lagrangian mul-tiplier technique with the Hoppeld network to solve a constrained optimization problem into which the original Bayesian estimation problem is reform...

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multiplie...