The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces

The augmented Lagrangian method for equality and inequality constraints in Hilbert spaces

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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: ,
Keywords: lagrange multipliers
Abstract:

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.

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