Mesh independence and fast local convergence of a primal-dual active-set method for mixed control-state constrained elliptic control problems

• Autores: Michael Hintermüller
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 49, Nº 1, 2007, págs. 1-38
• Idioma: inglés
• DOI: 10.1017/s1446181100012657
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• Resumen

  • A class of mixed control-state constrained optimal control problems for elliptic partial differential equations arising, for example, in Lavrentiev-type regularized state constrained optimal control is considered. Its numerical solution is obtained via a primal-dual active-set method, which is equivalent to a class of semi-smooth Newton methods. The locally superlinear convergence of the active-set method in function space is established, and its mesh independence is proved. The paper contains a report on numerical test runs including a comparison with a short-step path-following interior-point method and a coarse-to-fine mesh sweep, that is, a nested iteration technique, for accelerating the overall solution process. Finally, convergence and regularity properties of the regularized problems with respect to a vanishing Lavrentiev parameter are considered.