In this paper, we seek the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method and propose a family of conjugate gradient methods for unconstrained optimization. An improved Wolfe line search is also proposed, which can avoid a numerical drawback of the Wolfe line search and guarantee the global convergence of the conjugate gradient method under mild condi...

The conjugate gradient (CG) method is a popular Krylov space method for solving systems of linear equations of the form Ax = b, where A is a symmetric positive-deenite matrix. This method can be applied regardless of whether A is dense or sparse. In this paper, we show how restructuring compiler technology can be applied to transform a sequential, dense matrix CG program into a parallel, sparse...

This paper applies data selective updating to the Modified Conjugate Gradient algorithm. In search for a new conjugategradient-like filtering algorithm, two different approaches are developed: the first one results in the recently proposed set-membership affine projection (SM-AP) algorithm and the second one reduces the computational requirements of the modified congujate gradient algorithm whi...

In this paper we present a variant of the conjugate gradient (CG) algorithm in which we invoke a subspace minimization subproblem on each iteration. We call this algorithm CGSO for “conjugate gradient with subspace optimization”. It is related to earlier work by Nemirovsky and Yudin. We apply the algorithm to solve unconstrained strictly convex problems. As with other CG algorithms, the update ...

Conjugate gradient methods are a class of important methods for solving linear equations and nonlinear optimization. In our work, we propose a new stochastic conjugate gradient algorithm with variance reduction (CGVR) and prove its linear convergence with the Fletcher and Revves method for strongly convex and smooth functions. We experimentally demonstrate that the CGVR algorithm converges fast...

The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate all finite moments of a natural halting time when the random perturbation is drawn from the Laguerre unitary ensemble in a critical scaling regime explored in...

In this paper, a hybrid conjugate gradient algorithm with weighted preconditioner is proposed. The algorithm can efficiently solve the minimizing problem of general function deriving from finite element discretization of the p-Laplacian. The algorithm is efficient, and its convergence rate is meshindependent. Numerical experiments show that the hybrid conjugate gradient direction of the algorit...

This paper proposes to extend the band width of narrow band telephone speech signal by employing feed forward back propagation neural network. There are different types of faster training algorithm are available in the literature like Variable Learning Rate, Resilient Back propagation, Polak-Ribiére Conjugate Gradient , Conjugate Gradient with Powell/Beale Restarts , BFGS Quasi-Newton , One-Ste...