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...

Conjugate gradient methods are widely used for unconstrained optimization, especially large scale problems. Most of conjugate gradient methods don’t always generate a descent search direction, so the descent condition is usually assumed in the analyses and implementations. Dai and Yuan (1999) proposed the conjugate gradient method which generates a descent direction at every iteration. Yabe and...

Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a de...

A descent family of Dai–Liao conjugate gradient methods Saman Babaie-Kafaki & Reza Ghanbari a Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran c Faculty of Mathematical Sciences, Ferdowsi Universi...

Using an extension of some previously proposed modified secant equations in the Dai–Liao approach, a modified nonlinear conjugate gradient method is proposed. As interesting features, the method employs the objective function values in addition to the gradient information and satisfies the sufficient descent property with proper choices for its parameter. Global convergence of the method is est...

At the beginning of this century, which is characterized by huge flows emerging data, Dai and Liao proposed a pervasive conjugacy condition that triggered interest many optimization scholars. Recognized as sophisticated conjugate gradient (CG) algorithm after about two decades, here we share our visions thoughts on method in framework review study. In regard, first discuss modified Dai–Liao met...