A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. We discuss in this paper augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discu...

We present a formulation of the FETI substructuring method as a matrix preconditioning algorithm and report on theoretical results and practical experience in large scale parallel implementations. The method has quasi-optimal convergence properties: the condition number can be proved to be independent of the number of subdomains, and to grow at most polylogarithmically with the number of elemen...

We consider a FETI-DP formulation for the Stokes problem on nonmatching grids in 2D. The FETI-DP method is a domain decomposition method that uses Lagrange multipliers to match the solutions continuously across the subdomain boundaries in the sense of dual-primal variables. We use the mortar matching condition as the continuity constraints for the FETI-DP formulation. Moreover, to satisfy the c...

The ability of a multibody dynamic model to accurately predict the response of a physical system relies heavily on the use of appropriate system parameters in the mathematical model. Thus, the identification of unknown system parameters (or parameters that are known only approximately) is of fundamental importance. If experimental measurements are available for a mechanical system, the paramete...

In this paper, the variational iteraton method is used for solving the Generalized HirotaSatsuma Coupled KdV ( GHS KdV ) equations. In this method general Lagrange multipliers are introduced to construct correction functionals for the models.In the current paper, we are applied this technique on interesting and important model.The results are compared with exact solution.

This paper introduces a genetic algorithm enhanced with a trap escaping strategy derived from the dual information presented as discrete Lagrange multipliers. When the genetic algorithm is trapped into a local optima, the Discrete Lagrange Multiplier method is called for the best individual found. The information provided by the Lagrangian method is unified, in the form of recombination, with t...

Satissability is a class of NP-complete problems that model a wide range of real-world applications. These problems are diicult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method for solving satis-ability problems. We de...