Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent

Authors:
William W. Hager;Hongchao Zhang
Affiliations:
University of Florida, Gainesville, FL;University of Florida, Gainesville, FL
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2006

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Abstract

Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition gTkdk ≤ −7/8 ‖gk‖2 and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.