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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 denned 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.
Original language  English 

Pages (fromto)  674703 
Number of pages  30 
Journal  SIAM Journal on Optimization 
Volume  6 
Issue number  3 
Publication status  Published  1 Aug 1996 
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Projects


LANCELOT: LANCELOT, a package for the solution of largescale nonlinear optimization problems
TOINT, P., SARTENAER, A., Gould, N. I. M. & Conn, A.
1/09/87 → 1/09/00
Project: Research
Student Theses

On some strategies for handling constraints in nonlinear optimization
Author: Sartenaer, A., 1991Supervisor: Toint, P. (Supervisor), Conn, A. (External person) (Jury), Sachs, E. (External person) (Jury), Nguyen, V. H. (Jury) & Strodiot, J. (Jury)
Student thesis: Doc types › Doctor of Sciences