Global Convergence of a Nonsmooth Newton Method for Control-State Constrained Optimal Control Problems
Global Convergence of a Nonsmooth Newton Method for Control-State Constrained Optimal Control Problems
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DOI：
10.1137/060657546
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发表时间：
2008-02
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影响因子：
--
通讯作者：
M. Gerdts
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文献类型：
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作者：
M. Gerdts
我们研究了一种非光滑牛顿方法，用于求解受混合控制状态约束的最优控制问题。必要条件以局部最低原则规定。通过使用 Fischer-Burmeister 函数，局部最小原理被转换为适当 Banach 空间中的等效非线性和非光滑方程。该非线性非光滑方程通过非光滑牛顿法求解。我们证明了在一定规律性条件下的全局收敛性和局部超线性收敛性。全局化方法基于残差范数平方的最小化。瑞利问题的数值示例对本文进行了总结。
We investigate a nonsmooth Newton method for the numerical solution of optimal control problems subject to mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer-Burmeister function the local minimum principle is transformed into an equivalent nonlinear and nonsmooth equation in appropriate Banach spaces. This nonlinear and nonsmooth equation is solved by a nonsmooth Newton's method. We prove the global convergence and the locally superlinear convergence under certain regularity conditions. The globalized method is based on the minimization of the squared residual norm. Numerical examples for the Rayleigh problem conclude the article.