The spectral form of the Dai-Yuan conjugate gradient algorithm

Conjugate Gradient (CG) methods comprise a class of unconstrained optimization algorithms which are characterized by low memory requirements and strong local and global convergence properties. Most of CG methods do not always generate a descent search directions, so the descent or sufficient descent condition is usually assumed in the analysis and implementations. By assuming a descent and pure conjugacy conditions a new version of spectral Dai-Yuan (DY) non-linear conjugate gradient method introduced in this article. Descent property for the suggested method is proved and numerical tests and comparisons with other methods for large-scale unconstrained problems are given.