The Primal-Dual Active Set Strategy as a Semismooth Newton Method
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- 1 January 2002
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 13 (3) , 865-888
- https://doi.org/10.1137/s1052623401383558
Abstract
International audienceThis 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 L p-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 functionsKeywords
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