In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obt...

The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...

We introduce a simple local atomic structure optimization algorithm which is significantly faster than standard implementations of the conjugate gradient method and often competitive with more sophisticated quasi-Newton schemes typically used in ab initio calculations. It is based on conventional molecular dynamics with additional velocity modifications and adaptive time steps. The surprising e...

In this paper, a new weighted short-step primal-dual interior point algorithm for convex quadratic optimization (CQO) problems is presented. The algorithm uses at each interior point iteration only full-Newton steps and the strategy of the central path to obtain an ε-approximate solution of CQO. This algorithm yields the best currently wellknown theoretical iteration bound, namely, O( √ n log ε...

In this paper, we present a new path-following interior-point algorithm for *( ) P κ -horizontal linear complementarity problems (HLCPs). The algorithm uses only full-Newton steps which has the advantage that no line searchs are needed. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, (1 ) log n O n κ ε   +     , which is as ...

We propose to find the propagation constants of modes in layered media by means of signal identification methods. To this effect we employ Cauchy’s theorem, conformal mapping and Fast Fourier Transform (FFT) techniques to generate relevant Hankel moments, afterwards to be processed with selected signal identification algorithms. The method, terminated by a few Newton steps, provides a batch of ...

Michael Shub and Steve Smale Abstra t. We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of n homogeneous polynomial equations in n + 1 complex variables of fixed degrees will find all the roots of the system. We also extend the framework of our analysis to cover the classical implicit function theorem and revisit the condition n...

Kent and O'Quigley (1988) apply the concept of information gain to define a measure of dependence (R-squared measure) between explanatory variables and a censored response variable within the framework of the Cox model. Two SAS macros to calculate this measure are presented. The first one is based on a Newton-Raphson search and makes use of the SAS IML procedure. The second one is a simple grid...

We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity patt...

An inversion procedure for obtaining speeds, attenuation, densities, and thicknesses for a layered medium is described. The inversion is carried out using the least-squares technique and the forward modeling is based on SAFARI. The optimization is a hybrid method combining the global genetic algorithms and the local Gauss-Newton method. This is done by taking several gradient steps between each...