Global Convergence of Shortest-Residual Family of Conjugate Gradient Methods Without Line Search

Abstract

The shortest-residual family of conjugate gradient methods was first proposed by Hestenes and was studied by Pytlak, and Dai and Yuan. Recently, a no-line-search scheme in conjugate gradient methods was given by Sun and Zhang, and Chen and Sun. In this paper, we show the global convergence of two shortest-residual conjugate gradient methods (FRSR and PRPSR) without line search. In addition, computational results are presented to show that the methods with line search have similar numerical behavior to the methods without line search.

Optimal atomic-resolution structures of prion AGAAAAGA amyloid fibrils

“…Here, we would like to use the hybrid local and global optimization search methods to investigate the optimal atomic-resolution amyloid fibril models in hopes that the findings thus obtained may be of use for controlling prion diseases. Using the traditional local search steepest descent and conjugate gradient [Li and Chen, 2005, Sun and Zhang, 2001, Zhu and Chen, 2008] methods hybridized with the standard global search simulated annealing method [Horst et al, 2003, Yiu et al, 2004, zhang (2011a) successfully constructed three optimal atomic-resolution structures of prion AGAAAAGA amyloid fibrils. These structures were constructed based on the breakthrough work of [Sawaya et al, 2007].…”