Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints

Authors:
A. R. Conn;N. Gould;A. Sartenaer;Ph. L. Toint
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Optimization
Year:
1996

Citing 0
Cited 7

Convergence properties of augmented Lagrangian methods for constrained global optimization

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Bilinear factorization via augmented lagrange multipliers

ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
An augmented Lagrangian fish swarm based method for global optimization

Journal of Computational and Applied Mathematics
A parallel, asynchronous method for derivative-free nonlinear programs

ICMS'06 Proceedings of the Second international conference on Mathematical Software
Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

Computational Optimization and Applications
Saddle points of general augmented Lagrangians for constrained nonconvex optimization

Journal of Global Optimization
An inexact restoration strategy for the globalization of the sSQP method

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

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 each subproblem the augmented Lagrangian is approximately minimized in the region defined by the linear constraints. A subproblem is terminated as soon as a stopping condition is satisfied. The stopping rules that we consider here encompass practical tests used in several existing packages for linearly constrained optimization. Our algorithm also allows different penalty parameters to be associated with disjoint subsets of the general constraints. In this paper, we analyze the convergence of the sequence of iterates generated by such an algorithm and prove global and fast linear convergence as well as show that potentially troublesome penalty parameters remain bounded away from zero.