Article ID: | iaor1991711 |
Country: | Netherlands |
Volume: | 46 |
Issue: | 3 |
Start Page Number: | 341 |
End Page Number: | 360 |
Publication Date: | Apr 1990 |
Journal: | Mathematical Programming (Series A) |
Authors: | Ito K., Kunisch K. |
Keywords: | lagrange multipliers |
In this paper the authors consider an augmented Lagrangian method for the minimization of a nonlinear functional in the presence of an equality constraint whose image space is in a Hilbert space, an inequality constraint whose image space is finite dimensional, and an affine inequality constraint whose image space is in an infinite dimensional Hilbert space. They obtain local convergence of this method without imposing strict complementarity conditions when the equality, as well as the inequality constraint with finite dimensional image space are augmented. To the author’s knowledge this result even generalizes the convergence results which are known when all spaces are finite dimensional.