The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

To accelerate molecular dynamics simulations, it is common to impose holonomic constraints on the hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thereby allowing longer total simulation times. The imposition of such constraints results in an aditional set of N(c) equations (the equations of constraint) and unknowns (their assoc...

The Support Vector Machine (SVM) idea has attracted recent attention in solving classiication and regression problems. As an example based method, SVMs distinguish two point classes by nding a separating boundary layer, which is determined by points that become known as Support Vectors (SVs). While the computation of the separating boundary layer is formulated as a linearly constrained Quadrati...

We consider an inventory distribution system consisting of one warehouse and multiple retailers. The retailers face random demand and are supplied by the warehouse. The warehouse replenishes its stock from an external supplier. The objective is to minimize the total expected replenishment, holding and backlogging cost over a finite planning horizon. The problem can be formulated as a dynamic pr...

A number of nonparametric methods exist when studying the population and its parameters in the situation when the distribution is unknown. Some of them such as "resampling bootstrap method" are based on resampling from an initial sample. In this article empirical likelihood approach is introduced as a nonparametric method for more efficient use of auxiliary information to construct...

We study the convergence of the finite element method with Lagrange multipliers for approximately solving the Dirichlet problem for a second-order elliptic equation in a plane domain with piecewise smooth boundary. Assuming mesh refinements around the corners, we construct families of boundary subspaces that are compatible with triangular Lagrange elements in the interior, and we carry out the ...

A class of quadratic optimization problems in Hilbert spaces is considered, where pointwise box constraints and constraints of bottleneck type are given. The main focus is to prove the existence of regular Lagrange multipliers in L-spaces. This question is solved by investigating the solvability of a Lagrange dual quadratic problem. The theory is applied to different optimal control problems fo...

The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly dependent equations are also allowed. Both algorithms use the method of Lagrange multipliers to transform the original SLAE into a positively determined functio...