Nonlinear Conjugate Gradient Methods for Unconstrained Test Functions through an Approximate Wolfe Line Search

Abstract

The nonlinear conjugate gradient method stands out as a potent iterative
approach for tackling unconstrained large-scale optimization problems. A
crucial aspect of any conjugate gradient algorithm lies in determining an
optimal step length, a task for which various strategies have been put forth.
To assess and contrast the performance of the approximate Wolfe line
search technique, we conducted a numerical test across nine variants of
nonlinear conjugate gradient methods. Through our experiments, a notable
finding emerged: the Dai-Yuan nonlinear conjugate gradient method
demonstrated a swifter convergence compared to its counterparts. The
utilization of the approximate Wolfe line search technique, coupled with the
distinctive features of the Dai-Yuan variant, contributed to its enhanced
efficiency in navigating the optimization landscape. This empirical
exploration sheds light on the nuanced dynamics within nonlinear conjugate
gradient methods and underscores the significance of the selected strategy
for approximating the Wolfe line search. The observed faster convergence
of the Dai-Yuan method not only validates its efficacy but also suggests its
potential applicability in scenarios where rapid and effective optimization is
paramount.