QUADRATIC AND SUPERLINEAR CONVERGENCE OF THE HUSCHENS METHOD FOR NONLINEAR LEAST-SQUARES PROBLEMS

This paper is concerned with quadratic and superlinear convergence of structured quasi-Newton methods for solving nonlinear least squares pr oblems. These methods make use of a special structure of the Hessian m atrix of the objective function. Recently, Huschens proposed a new kin d of structured quasi-Newton methods and dealt with the convex class o f the structured Broyden family, and showed its quadratic and superlin ear convergence properties for zero and nonzero residual problems, res pectively. In this paper, we extend the results by Huschens to a wider class of the structured Broyden family. We prove local convergence pr operties of the method in a way different from the proof by Huschens.