Related papers: A convergence condition for Newton-Raphson method
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
In path-following methods for conic programming knowledge of the performance of the (damped) Newton method at finite distances from the minimizer of a self-concordant function is crucial for the tuning of the parameters of the method. The…
In this paper, by combining the algorithm New Q-Newton's method - developed in previous joint work of the author - with Armijo's Backtracking line search, we resolve convergence issues encountered by Newton's method (e.g. convergence to a…
The numerical integration of an analytical function $f(x)$ using a finite set of equidistant points can be performed by quadrature formulas like the Newton-Cotes. Unlike Gaussian quadrature formulas however, higher-order Newton-Cotes…
The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…
Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…
An iterative optimization method applied to a function $f$ on $\mathbb{R}^n$ will produce a sequence of arguments $\{\mathbf{x}_k\}_{k \in \mathbb{N}}$; this sequence is often constrained such that $\{f(\mathbf{x}_k)\}_{k \in \mathbb{N}}$…
In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…
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…
This article proposes new perspectives for developing derivative based numerical algorithms, supported by the introduction of a generalized derivative operators. It demonstrates that these operators have the potential to enhance and extend…
We explore a family of numerical methods, based on the Steffensen divided difference iterative algorithm, that do not evaluate the derivative of the objective functions. The family of methods achieves second-order convergence with two…
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying $f(a)-f(b)\equiv0 \pmod {(a-b)}$ for all $a>b$. We characterize this class of functions…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
Algorithms based on the hard thresholding principle have been well studied with sounding theoretical guarantees in the compressed sensing and more general sparsity-constrained optimization. It is widely observed in existing empirical…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
In this paper, we consider the shift-inverse method with Richardson iteration step for the eigenvalue problems. It will be shown that the convergence speed depends heavily on the eigenvalue gap between the desired eigenvalue and undesired…
Traditionally, assessing the accuracy of inference based on regression quantiles has relied on the Bahadur representation. This provides an error of order $n^{-1/4}$ in normal approximations, and suggests that inference based on regression…