The Primal-Dual Active Set Strategy as a Semismooth Newton Method

Authors:
M. Hintermüller;K. Ito;K. Kunisch
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
2002

Citing 0
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Abstract

This paper addresses complementarity problems motivated by constrained optimal control problems. It is shown that the primal-dual active set strategy, which is known to be extremely efficient for this class of problems, and a specific semismooth Newton method lead to identical algorithms. The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept. This leads to new local convergence results of the primal-dual active set strategy. Global unconditional convergence results are obtained by means of appropriate merit functions.