We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties.

In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences , by a trust region-cg algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while ...

We consider methods for large-scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two-norm trust-region constraint. The Steihaug–Toint method uses the conjugate-gradient method to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the constraint boundary. Howev...

We describe an optimization method for large-scale nonnegative regularization. The method is an interiorpoint iteration that requires the solution of a large-scale and possibly ill-conditioned parameterized trust-region subproblem at each step. The method relies on recently developed techniques for the large-scale trust-region subproblem. We present preliminary numerical results on image restor...

In this paper, a non-monotone adaptive trust region method for the system of non-linear equations is proposed, in part, which is based on the technique in [9]. The local and global convergence properties of non-monotone adaptive trust region method are proved under favorable conditions. Some numerical experiments show that the method is effective.