Yet another polynomial preconditioner for the conjugate gradient algorithm

Another nonlinear conjugate gradient algorithm for unconstrained optimization

A nonlinear conjugate gradient algorithm which is a modification of the Dai and Yuan [Y.H. Dai and Y, Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), pp.177-182.] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter k δ is proposed. The parameter k δ is computed by means of the conj...

An Efficient Conjugate Gradient Algorithm for Unconstrained Optimization Problems

In this paper, an efficient conjugate gradient method for unconstrained optimization is introduced. Parameters of the method are obtained by solving an optimization problem, and using a variant of the modified secant condition. The new conjugate gradient parameter benefits from function information as well as gradient information in each iteration. The proposed method has global convergence und...

A new hybrid conjugate gradient algorithm for unconstrained optimization

In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

Yet Another System For Algorithm

A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method

A method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix A is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations. It is proved that in exact arithmetic the preconditioner is well defined if A is an H-matrix. The results of numerical experiments are pre...