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...

An error analysis is presented for the approximation of the statiornary Stokes equations by a finite element method using Lagrange multipliers.

In this paper we introduce a modified penalty function (MPF) method for solving a problem which minimizes a nonlinear programming subject to inequality constraints. Basically, this method is a combination of the modified penalty methods and the Lagrangian methods. It treats inequality constraints with a modified penalty function and avoids the indifferentiability of max {x, 0}. This method alte...

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

In this talk we consider the finite element discretization of the Immersed Boundary Method (IBM) introduced by Peskin [6] for fluid-structure interaction problems. With respect to the original finite differences discretization the finite element approach can take advantage from the variational formulation in handling the Dirac delta function which takes into account the presence of the structur...

Isogeometric analysis (IGA) is a novel computational approach recently developed by Hughes et al. [1]with the aim of integrating computer aided design (CAD) into structural analysis. It uses non uniform rational B-splines (NURBS) for both description of the geometry and approximation of thesolution field. NURBS are the most common basis functions in the CAD systems. Using CAD basis functions di...

Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is th...

The primal hybrid method for solving second-order elliptic equations is extended from finite element approximations to general bases. Variational techniques are used to show convergence of approximations to the solution of the homogeneous Dirichlet problem for selfadjoint equations. Error estimates are obtained and examples are given. Introduction Lagrange multipliers have been employed to defi...