At present, most of the control methods of the lower extremity exoskeleton carrying robot require to calculate the system’s dynamic equation and create the control quantity at each moment, which don’t make full use of the repeatability feature of human movement and inevitably causes the delay on the dynamic response of the system. In this paper, utilizing the dynamic repeat characteristics of h...

Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically ...

While generalized equations with differentiable single-valued base mappings and the associated Josephy–Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush-Kuhn-Tucker optimality systems). We introduce for the general semismooth case appropriate notion...

First-order methods such as SGD and Adam are popularly used in training Neural networks. On the other hand, second-order have shown to better performance faster convergence despite their high computational cost by incorporating curvature information. While determine step size line search approaches, first-order achieve efficient learning devising a way adjust size. In this paper, we propose new...

This paper proposes an implementable proximal quasi-Newton method for minimizing a nondifferentiable convex function f in <n . The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point p(xk) of xk to define a vk ∈ ∂ k f(p(xk))with k ≤ α‖vk‖,where α is a constant. The method monitors the reduction in the value ...

This paper examines the e ectiveness of using a quasi-Newton based training of a feedforward neural network for forecasting. We have developed a novel quasi-Newton based training algorithm using a generalized logistic function. We have shown that a well designed feed forward structure can lead to a good forecast without the use of the more complicated feedback/feedforward structure of the recur...

Finding roots of nonlinear algebraic systems is paramount to many applications in applied mathematics because the physical laws of interest are usually nonlinear. If the functions comprising a system are complicated it is beneficial to reduce computing the functions as much as possible. The following describes a quasi-Newton root solver called Broyden Approximate Norm Descent, or ’BroydenAND’, ...

A quasi-Newton Method is used to simultaneously relax the internal coordinates and lattice parameters of crystals under pressure. The symmetry of the crystal structure is preserved during the relaxation. From the inverse of the Hessian matrix, elastic properties and some optical phonon frequencies at the Brillouin zone center can be estimated. The e ciency of the method is demonstrated for sili...

In this paper we give the results found in solving consistent sparse systems of nonlinear equations by an inexact Newton and Quasi-Newton method both combined with a block iterative row-projection linear solver of Cimmino-type. A simple partitioning of the Jacobian matrix was used for solving two nonlinear test problems, that is a tridiagonal problem of size n = 131072 and a nonlinear Poisson p...

We consider the problem of solving linear systems of equations with limited-memory members of the restricted Broyden class and symmetric rank-one matrices. In this paper, we present various methods for solving these linear systems, and propose a new approach based on a practical implementation of the compact representation for the inverse of these limited-memory matrices. Using the proposed app...