We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in different ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a sequence of subproblems; in each subprob...

We consider the two-level uncapacitated facility location problem with singleassignment constraints (TUFLP-S), a problem that arises in industrial applications in freight transportation and telecommunications. We present a new Lagrangian relaxation approach for the TUFLP-S, based on solving a single-level uncapacitated facility location problem (UFLP) as the Lagrangian subproblem. We also devel...

Abstract The Lagrangian vortex particle method for two-dimensional flow simulation around airfoils is considered. Generally, the most time-consuming operation in particles interaction simulation, especially if it performed directly “point-to-point” all pairs of particles. result such convective velocities. This problem similar to N-body and has squared computational complexity O(N 2 ). only eff...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

ABSTRACT We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in different ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a sequence of subproblems; in eac...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover. We show that for Partial Cover in general no algorithm that uses Lagrangian relaxation and a Lagrangian Multiplier Preserving (LMP) α-approximation as a black box can yield an approximation factor better than 4 3 α. This match...

A new exact solution algorithm is proposed for the Degree-Constrained Minimum Spanning Tree Problem. The algorithm involves two combined phases. The first one contains a Lagrangian Relaxand-Cut procedure while the second implements a Branch-and-Cut algorithm. Both phases rely on a standard formulation for the problem, reinforced with Blossom Inequalities. An important feature of the proposed al...

Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? ...

A branch and bound algorithm is proposed for finding an approximate global optimum of quadratic functions over a bounded polyhedral set. The algorithm uses Lagrangian duality to obtain lower bounds. Preliminary computational results are reported.