牛顿法和伴随理论在半线性发展方程描述的参数系统的系统辩识中的应用

应用Hilbert空间中的最优化方法的牛顿法和伴随理论来研究一半线性发展方程描述的参数系统的系统参数辩识，并给出了牛顿法二次收敛性的一种证明．利用伴随理论和基本解的方法得到了目标泛函关于参数的海色算子简单表达式．最后给出了一个算法及一简单的数值例子来验证这个算法．

Application of the Newton Method and Adjoint Theory to Identification of a Semi-linear Evolution System

The Newton method in infinite dimensional optimization and the adjoint theory ar e used to identify parameters involved in a semi-linear evolution system, and a proof of local quadratic convergence of the Newton method is given. By adjoint theory and the fundamental solution methods, author obtain a sample expression of the Hesse operator of the cost function. Finally, an algorithm is given and a numerical example is provided to verify t he algorithm.