A Class Of New Factorized Quasi-Newton Methods For Nonlinear Least Squares Problems

Nonlinear least squares problem is extensively used in experimentations ,projects and so on. As an unconstrained optimization problem, it has a lot of methods to solve for its special structure. And Quasi-Newton method is based on the quasi-Newton equation , which is often used in solving optimization problems.In this paper ,we present a class of new factorized quasi-Newton algorithms for nonlinear least squares problems which are based on new quasi-Newton equation and factorized quasi-Newton method. New factorized quasi-Newton equation not only uses the gradient information of the objection function ,but also uses the function information . It is superior to the traditional factorized quasi-Newton equation in the sense that it has a higher-order curvature approximation.The local superlinear convergence of line search type algorithm are proved under some condition. And trust region type algorithm with memoryless technology not only satisfies new factorized quasi-Newton equation, but also saves much storage and algebraic operations than the original factorized quasi-Newton methods.we prove it posses the global convergence and the local superlinear convergence under some condition.Numerical experiments indicate that the new algorithms are more feasible and effective .