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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer-Verlag

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10.1002/2014JG002861

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1436-4646

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Primaldual interiorpoint methods for PDEconstra

Authors: Michael Ulbrich Stefan Ulbrich
Publish Date: 2007/07/19
Volume: 117, Issue: 1-2, Pages: 435-485
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Abstract

This paper provides a detailed analysis of a primaldual interiorpoint method for PDEconstrained optimization Considered are optimal control problems with control constraints in L p It is shown that the developed primaldual interiorpoint method converges globally and locally superlinearly Not only the easier L ∞setting is analyzed but also a more involved L q analysis q  ∞ is presented In L ∞ the set of feasible controls contains interior points and the Fréchet differentiability of the perturbed optimality system can be shown In the L q setting which is highly relevant for PDEconstrained optimization these nice properties are no longer available Nevertheless a convergence analysis is developed using refined techniques In parti cular twonorm techniques and a smoothing step are required The L q analysis with smoothing step yields global linear and local superlinear convergence whereas the L ∞analysis without smoothing step yields only global linear convergence

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