Article ID: | iaor20003787 |
Country: | Netherlands |
Volume: | 14 |
Issue: | 1 |
Start Page Number: | 55 |
End Page Number: | 74 |
Publication Date: | Jul 1999 |
Journal: | Computational Optimization and Applications |
Authors: | Goldfarb D., Polyak R., Scheinberg K., Yuzefovich I. |
Keywords: | lagrange multipliers |
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 modified barrier term and equalities with an augmented Lagrangian term. The MBAL method alternatively minimizes the MBAL function in the primal space and updates the Lagrange multipliers. For a large enough fixed barrier-penalty parameter the MBAL method is shown to converge