Quasi-Newton methods for nonlinear least squares focusing on curvatures (Q1293245)

A new quasi-Newton method for nonlinear least squares problems is proposed. In these problems the Hessian is composed of both a linear term (first-order information) and a nonlinear term (second-order information). The objective of this paper is to propose quasi-Newton methods that only updates the nonlinearities. Two advantages of the method are accomplished by utilizing special geometrical properties in the problem class. First, fast convergence is established for well-conditioned problems by interpolating both the current and the previous step in each iteration. Second, high accuracy is achieved for certain difficult problems, such as ill-conditioned problems and problems with large curvatures in the tangent space. Numerical results for artificial problems and standard test problems are presented and discussed.