In this paper, a generalized Hoppeld model with continuous neurons using Lagrange multipliers, originally introduced in 12], is thoroughly analysed. We have termed the model the Hoppeld-Lagrange model. It can be used to resolve constrained optimization problems. In the theoretical part, we present a simple explanation of a fundamental energy term of the continuous Hoppeld model. This term has c...

2 Methods 2 2.1 Lagrange Multiplier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Pegging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Interior-Point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.2 Interior-Point Algorithm ....

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

This paper suggests a robust LM (Lagrange Multiplier) test for spatial error model which not only reduces the influence of spatial lag dependence immensely, but also presents robust to changes of spatial layouts and distribution misspecification. Monte Carlo simulation results imply that existing LM tests have serious size and power distortion with the presence of spatial lag dependence, group ...

In this paper, we suggest a new technique which uses Lagrange polynomials to get derivative-free iterative methods for solving nonlinear equations. With the use of the proposed technique and Steffens on-like methods, a new optimal fourth-order method is derived. By using three-degree Lagrange polynomials with other two-step methods which are efficient optimal methods, eighth-order methods can b...

A certain functional–difference equation that Runyon encountered when analyzing a queuing system was solved in a combined effort of Morrison, Carlitz, and Riordan. We simplify that analysis by exclusively using generating functions, in particular the kernel method, and the Lagrange inversion formula.

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...