An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of the method...

We revisit the classic Horn and Schunck optical flow method, with focus on its interpretation as a Gauss-Newton (GN) minimisation of a non-linear energy. This is in contrast to the traditional derivation by linearisation of the brightness constancy assumption. The proposed interpretation provides a much simpler derivation and a better theoretical understanding of the method, and allows for its ...

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm i...

We propose an iterative method that solves constrained linear least-squares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally...

Kernel logistic regression (KLR) is a powerful and flexible classification algorithm, which possesses an ability to provide the confidence of class prediction. However, its training—typically carried out by (quasi-)Newton methods—is rather timeconsuming. In this paper, we propose an alternative probabilistic classification algorithm called Least-Squares Probabilistic Classifier (LSPC). KLR mode...