Primal-dual interior-point methods for PDE-constrained optimization

被引:0
作者
Michael Ulbrich
Stefan Ulbrich
机构
[1] Zentrum Mathematik M1,Chair of Mathematical Optimization
[2] TU München,TU Darmstadt, Fachbereich Mathematik
[3] AG10: Nonlinear Optimization and Optimal Control,undefined
来源
Mathematical Programming | 2009年 / 117卷
关键词
Primal-dual interior point methods; PDE-constraints; Optimal control; Control constraints; Superlinear convergence; Global convergence; 90C51; 90C48; 49M15; 65K10;
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中图分类号
学科分类号
摘要
This paper provides a detailed analysis of a primal-dual interior-point method for PDE-constrained optimization. Considered are optimal control problems with control constraints in Lp. It is shown that the developed primal-dual interior-point method converges globally and locally superlinearly. Not only the easier L∞-setting is analyzed, but also a more involved Lq-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 Lq-setting, which is highly relevant for PDE-constrained optimization, these nice properties are no longer available. Nevertheless, a convergence analysis is developed using refined techniques. In parti- cular, two-norm techniques and a smoothing step are required. The Lq-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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页码:435 / 485
页数:50
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