An efficient modification of the Hestenes-Stiefel nonlinear conjugate gradient method with restart property
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Date
2016
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Publisher
Journal of Inequalities and Applications
Abstract
The conjugate gradient (CG) method is one of the most popular methods to solve
nonlinear unconstrained optimization problems. The Hestenes-Stiefel (HS) CG
formula is considered one of the most efficient methods developed in this century. In
addition, the HS coefficient is related to the conjugacy condition regardless of the line
search method used. However, the HS parameter may not satisfy the global
convergence properties of the CG method with the Wolfe-Powell line search if the
descent condition is not satisfied. In this paper, we use the original HS CG formula
with a mild condition to construct a CG method with restart using the negative
gradient. The convergence and descent properties with the strong Wolfe-Powell
(SWP) and weak Wolfe-Powell (WWP) line searches are established. Using this
condition, we guarantee that the HS formula is non-negative, its value is restricted,
and the number of restarts is not too high. Numerical computations with the SWP line
search and some standard optimization problems demonstrate the robustness and
efficiency of the new version of the CG parameter in comparison with the latest and
classical CG formulas. An example is used to describe the benefit of using differen
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Keywords
conjugate gradient method, Wolfe-Powell line search, Hestenes-Stiefel formula, restart condition, performance profile
Citation
Vol.2016(1);