In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve class of nonsmooth nonconvex composite optimization problems. We assume that the gradient smooth part objective function can only be approximated by oracles. The proposed combines general higher order steps derived from an underlying proximal type fixed-point equation with additional guarantee convergence. Ba...

Some algorithms in the primal have been recently proposed for training support vector machines. This letter follows those studies and develops a recursive finite Newton algorithm (IHLF-SVR-RFN) for training nonlinear support vector regression. The insensitive Huber loss function and the computation of the Newton step are discussed in detail. Comparisons with LIBSVM 2.82 show that the proposed a...

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...

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...

A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high convergence orders were characterized by Dennis and Moré [Math. Comp. 28 (1974), 549–560]. The inexact Newton method constitutes another such model, since it assumes that at each step the linear systems are only approximat...

A fundamental computational procedure in practically all areas of scientific computing is the calculation of the Newton step (in n-dimensions). In many cases this computation represents the dominant cost in the overall computing task. Typically the Newton step computation breaks down into two separable subtasks: calculation of the Jacobian (or Hessian) matrix along with the right-hand-side, and...

We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward ...