In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem.We tackle the problem using duality concept, differently from traditional approaches. Ourmethod is based on Lagrangian relaxation. Lagrangemultipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the cap...

Degrees of freedom which are Lagrange multipliers anse in the finite element approximation of mixed vanational problems. When these degrees of freedom are "local", the intioduction of a small perturbation {conespondinq hv duality to a penalty function) enables the élimination of these unknouns at the element level We fitst examine this method in the continuons case and show that the solution of...

In this paper, an importance sampling method – cross entropy method is presented to deal with solving support vector machines (SVM) problem for multiclass classification cases. Using one-against-rest (OAR) and one-against-one (OAO) approaches, several binary svm classifiers are constructed and combined to solve multiclass classification problems. For each binary SVM classifier, the cross entrop...

We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization probl...

An embedding domain method for mixed boundary value problems is derived and applied to a class of shape optimization problems. The derivative of the cost with respect to the shape is characterized in terms of the Lagrange multipliers for the pri-mal and the adjoint problem. Numerical results illustrating the eeciency of the method which is related to a mixed nite element method are presented.

The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...

Starting from second-order conditions for C scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof...

We combine the controllability and fictitious domain methods to compute time-periodic solution for a wave equation describing scattering by an obstacle. The fictitious domain method uses distributed Lagrange multipliers to satisfy the Dirichlet boundary condition on the scatterer. The controllability technique leads to an optimization problem which we solve with a preconditioned conjugate gradi...