A new nonlinear conjugate gradient method, based on Perry’s idea, is presented. And it is shown that its sufficient descent property is independent of any line search and the eigenvalues of $P_{k+1}^{\T}P_{k+1}$ are bounded above, where $P_{k+1}$ is the iteration matrix of the new method. Thus, the global convergence is proven by the spectral analysis for nonconvex functions when the line search fulfills the Wolfe conditions. Preliminary numerical results for a set of 720 unconstrained optimization test problems verify the performance of the new method and show that it is competitive with the CG\_DESCENT method.
Citation
Technical Report of Optimization No: 2010-11-08, Control Theory Laboratory,Department of Mathematics, University of Tianjin.