We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based...

In this paper we present a Newton scoring algorithm for the maximum likelihood separation and direction of arrival estimation of constant modulus signals, using a calibrated array. The main technical step is the inversion of the Fisher information matrix, and an analytic formula for the update step in the Newton method. We present the algorithm based on the derived update and discuss potential ...

We propose a new algorithm for the non-negative ICA problem, based on the rotational nature of optimization over a set of square orthogonal (orthonormal) matrices W, i.e. where W W = WW = In. Using a truncated Fourier expansion of J(t), we obtain a Newton-like update step along the steepest-descent geodesic, which automatically approximates to a usual (Taylor expansion) Newton update step near ...

Naive implementations of Newton's method for unconstrained N-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost like N 3 as N increases. However, if the inherent recursive structure of the Bolza problem is properly exploited, the cost of computing a Newton step will increase only linearly with N. The efficient Newton implementation scheme propos...

The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...

We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. T...

In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields a (practical) long-step algorithm. Both algorithms allow for ...

We explain an interface for the implementation of rate-independent elastoplasticity which separates the pointwise evaluation of the elastoplastic material law and the global solution of the momentum balance equation. The elastoplastic problem is discretized in time by the implicit Euler method and every time step is solved with a Newton iteration. For the discretization in space the material pa...

In this paper, we investigate the semismooth Newton and quasi-Newton methods for the minimization problem in the weighted `−regularization of nonlinear inverse problems. We propose the conditions for obtaining the convergence of two methods. The semismooth Newton method is proven to locally converge with superlinear rate and the semismooth quasi-Newton method is proven to locally converge at le...

Newton-Krylov methods, combination of Newton-like methods and Krylov subspace methods for solving the Newton equations, often need adequate preconditioning in order to be successful. Approximations of the Jacobian matrices are required to form preconditioners and this step is very often the dominant cost of Newton-Krylov methods. Therefore, working with preconditioners destroys in principle the...