A nonsmooth Newton's method for control-state constrained optimal control problems
A nonsmooth Newton's method for control-state constrained optimal control problems
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DOI：
10.1016/j.matcom.2008.02.018
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发表时间：
2008-12
期刊：
影响因子：
--
通讯作者：
M. Gerdts
中科院分区：
文献类型：
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作者：
M. Gerdts
我们研究了混合控制状态约束下的最优控制问题。必要条件是用局部极小值原理来描述的。利用Fischer-Burmeister函数将极小值原理转化为适当Banach空间中的一个等价的非线性非光滑方程。这个非线性和非光滑方程求解的非光滑牛顿的方法。我们将证明在一定的正则性条件下的局部二次收敛性，并提出一个全球化战略的基础上最小化的平方剩余范数。瑞利问题的一个数值例子结束了文章。
We investigate 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 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 will show the local quadratic convergence under certain regularity conditions and suggest a globalization strategy based on the minimization of the squared residual norm. A numerical example for the Rayleigh problem concludes the article.