In this paper we describe an on-line method of training neural networks which is based on solving the linearized least-squares problem using the pseudo-inverse for the underdetermined case. This Underdetermined Linearized Least Squares (ULLS) method requires significantly less computation and memory for implementation than standard higher-order methods such as the Gauss-Newton method or extende...

We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving p...

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton’s method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first ana...

Approximate Newton methods are standard optimization tools which aim to maintain the benefits of Newton’s method, such as a fast rate of convergence, while alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first analy...

In this work we address robust estimation in the bundle adjustment procedure. Typically, bundle adjustment is not solved via a generic optimization algorithm, but usually cast as a nonlinear leastsquares problem instance. In order to handle gross outliers in bundle adjustment the least-squares formulation must be robustified. We investigate several approaches to make least-squares objectives ro...

In this paper we present the results obtained in the solution of sparse and large systems of non-linear equations by inexact Newton methods combined with an block iterative row-projection linear solver of Cimmino-type. Moreover, we propose a suitable partitioning of the Jacobian matrix A. In view of the sparsity, we obtain a mutually orthogonal row-partition of A that allows a simple solution o...

We introduce a novel multiframe scene flow approach that jointly optimizes the consistency of the patch appearances and their local rigid motions from RGB-D image sequences. In contrast to the competing methods, we take advantage of an oversegmentation of the reference frame and robust optimization techniques. We formulate scene flow recovery as a global non-linear least squares problem which i...

Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the hessian of the function to iteratively find a local solution. Although fast, this strategy inevitably leeds to issues with poor local minima and missed global minima. In this paper ra...

In applying the level-set method developed in [Van den Berg and Friedlander, SIAM J. on Scientific Computing, 31 (2008), pp. 890–912 and SIAM J. on Optimization, 21 (2011), pp. 1201– 1229] to solve the fused lasso problems, one needs to solve a sequence of regularized least squares subproblems. In order to make the level-set method practical, we develop a highly efficient inexact semismooth New...