A Newton-type curvilinear search method for optimization

A Regularized Newton Method without Line Search for Unconstrained Optimization∗

In this paper, we propose a regularized Newton method without line search. The proposed method controls a regularized parameter instead of a step size in order to guarantee the global convergence. We demonstrate that it is closely related to the TR-Newton method when the Hessian of the objective function is positive definite. Moreover, it does not solve nonconvex problems but linear equations a...

A continuous Newton-type method for unconstrained optimization

In this paper, we propose a continuous Newton-type method in the form of an ordinary differential equation by combining the negative gradient and Newton’s direction. It is shown that for a general function f(x), our method converges globally to a connected subset of the stationary points of f(x) under some mild conditions; and converges globally to a single stationary point for a real analytic ...

An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

and Applied Analysis 3 rate of convergence under some additional assumptions, and it should be noted that we only use the approximate values of the objective function and its subgradients which makes the algorithm easier to implement. Some notations are listed below for presenting the algorithm. (i) ∂f(x) = {ξ ∈ Rn | f(z) ≥ f(x) + ξT(z − x), ∀z ∈ R}, the subdifferential of f at x, and each such...

A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization

A Curvilinear Search Method for p-Harmonic Flows on Spheres

The problem of finding p-harmonic flows arises in a wide range of applications including color image (chromaticity) denoising, micromagnetics, liquid crystal theory, and directional diffusion. In this paper, we propose an innovative curvilinear search method for minimizing p-harmonic energies over spheres. Starting from a flow (map) on the unit sphere, our method searches along a curve that lie...