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...

Increased electric energy demand is the major factor that cracks researchers to focus on electrical meet challenge. Accordingly, power loss should be minimized. Due this, Distribution Flexible Alternating Current Transmission System (DFACTS) and Distributed Generation (DG) must placed in an appropriate way distribution systems. Fuzzy-Lightning Search Algorithm (FLSA) has been proposed minimize ...

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...

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...