A Trust Region Method for Solving Distributed Parameter Identification Problems

Abstract

This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in many applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem. Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for ill-posed problems. Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising.