We consider projected Newton-type methods for solving large-scale optimization problems arising in machine learning and related fields. We first introduce an algorithmic framework for projected Newton-type methods by reviewing a canonical projected (quasi-)Newton method. This method, while conceptually pleasing, has a high computation cost per iteration. Thus, we discuss two variants that are m...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

one of the problems that sometimes occur in gas allocation optimization is instability phenomenon. this phenomenon reduces the oil production and damages downhole and surface facilities. different works have studied the stability and suggested some solutions to override it, but most of them (such as making the well intelligent) are very expensive and thus they are not applicable to many cases. ...

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...

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations applied to second order differential operators with nonlinear diffusion coefficient. Under mild assumptions arising in practical applications, an app...

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to mani...

More than a decade agao, Newton’s method has been proposed for constructing the convex best interpolant. Its local quadratic convergence has only been established recently by recasting it as the generalized Newton method for semismooth equations. It still remains mysterious that the Newton method coupled with line search strategies works practically well in global sense. Similar to the classica...

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost at each iteration while commanding a high convergence rate. In this work we propose two new efficient ...

This paper explores Wallis’s role as editor of Newton’s mathematical work. My objective is to understand how two mathematicians who held different views concerning mathematical method could nonetheless cooperate with one another quite effectively. Most notably, Wallis and Newton pursued different policies as far as the printing of algebra is concerned. In the 1690s Newton held the view that alg...

Newton law arising due to the gravity localized on the general singular brane embedded in AdS5 bulk is examined in the absence or presence of the 4d induced Einstein term. For the RS brane, apart from the subleading correction, Newton potential obeys 4d-type and 5d-type gravitational law at longand short-ranges if it were not for the induced Einstein term. The 4d induced Einstein term generates...