A new method used to prove the global convergence of the nonlinear conjugate gradient methods, the spectral method, is presented in this paper, and it is applied to a new conjugate gradient algorithm with sufficiently descent property. By analyzing the descent property, several concrete forms of this algorithm are suggested. Under standard Wolfe line searches, the global convergence of the new ...

NEURBT, a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. NEURBT is based on Møller’s scaled conjugate gradient algorithm which is a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the imple­ mentation are discussed such as the efficient computation ...

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the ...

Self-concordant functions are a special class of convex functions in Euclidean space introduced by Nesterov. They are used in interior point methods, based on Newton iterations, where they play an important role in solving efficiently certain constrained optimization problems. The concept of self-concordant functions has been defined on Riemannian manifolds by Jiang et al. and a damped Newton m...

This paper presents a conjugate gradient-based algorithm for feedback min–max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer NN. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient method...

Graphical processing units introduce the capability for large scale computation in the desk top environment. For the solution of linear systems of equations, much effort has been devoted to efficient implementation of Krylov subspace-based solvers in high performance computing environments. Here the focus is to improve the computational efficiency of the projected conjugate gradient algorithm. ...