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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 |
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Pages (from-to) | 674-703 |

Number of pages | 30 |

Journal | SIAM Journal on Optimization |

Volume | 6 |

Issue number | 3 |

Publication status | Published - 1 Aug 1996 |

## Fingerprint Dive into the research topics of 'Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints'. Together they form a unique fingerprint.

## Projects

## LANCELOT: LANCELOT, a package for the solution of large-scale 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