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...

Abstract In this paper, we suggest a new infeasible interior-point method (IIPM) for $$P_{*}(\kappa )$$ P ∗ ( κ ) -linear complementarity problem ( -LCP) based on class of kernel func...

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...

We propose a new distributed algorithm for empirical risk minimization in machine learning. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the resul...

We show how certain widely used multistep approximation algorithms can be interpreted as instances of an approximate Newton method. It was shown in an earlier paper by the second author that the convergence rates of approximate Newton methods (in the context of the numerical solution of PDEs) suuer from a \loss of derivatives", and that the subsequent linear rate of convergence can be improved ...

In this letter, we present a computational framework based on the use of the Newton and level set methods and tailored for the modeling of bubbles with surface tension in a surrounding Newtonian fluid. We describe a fully implicit and monolithic finite element method that maintains stability for significantly larger time steps compared to the usual explicit method and features substantial compu...

We present a method for solving polynomial equations over idempotent ω-continuous semirings. The idea is to iterate over the semiring of functions rather than the semiring of interest, and only evaluate when needed. The key operation is substitution. In the initial step, we compute a linear completion of the system of equations that exhaustively inserts the equations into one another. With func...

Newton’s method is one of the most famous numerical methods. Its origins, as the name suggests, lies in part with Newton, but the form familiar to us today is due to Simpson of “Simpson’s Rule” fame. Originally proposed to find the roots of polynomials it was Simpson who proposed using it for general nonlinear equations and for its use in optimization by finding a root of the gradient. Here we ...