Recently a new blind equalization method was proposed for the 16QAM constellation input inspired by the maximum entropy density approximation technique with improved equalization performance compared to the maximum entropy approach, Godard's algorithm, and others. In addition, an approximated expression for the minimum mean square error (MSE) was obtained. The idea was to find those Lagrange mu...

This thesis proposes a two-stage optimization for solving unit commitment. In the first stage, Lagrangian Relaxation (LR) method is used to solve unit commitment using a sub-gradient algorithm for updating Lagrange multipliers. In the second stage, Particle Swarm Optimization (PSO) is applied to update Lagrange multipliers in the Lagrangian Relaxation method (PSOLR). Lagrange multipliers soluti...

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange mul...

A new flexibility-based component mode synthesis method is presented, which is derived by approximating the partitioned equations of motion that employ a localized method of Lagrange multipliers. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without any redundancies at multiply connected interfac...

In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses rest...

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...

and there are no inequality constraints (i.e. there are no fi(x) i = 1, . . . , m). We simply write the p equality constraints in the matrix form as Cx− d = 0. The basic idea in Lagrangian duality is to take the constraints in (1) into account by augmenting the objective function with a weighted sum of the constraint functions. We define the Lagrangian L : R ×R ×R → R associated with the proble...

It is crucial to maximize marketing efficiency and customer satisfaction in personalized marketing. In this paper, we raise the multiple recommendation problem which occurs when performing several personalized campaigns simultaneously. We formulate the multi-campaign assignment problem to solve this issue and propose methods for solving the problem. The most notable element is the Lagrange mult...