A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems

Abstract EN

This paper further studies the WYL conjugate gradient (CG) formula with βkWYL≥0 and presents a three-term WYL CG algorithm, which has the sufficiently descent property without any conditions.

The global convergence and the linear convergence are proved; moreover the n-step quadratic convergence with a restart strategy is established if the initial step length is appropriately chosen.

Numerical experiments for large-scale problems including the normal unconstrained optimization problems and the engineer problems (Benchmark Problems) show that the new algorithm is competitive with the other similar CG algorithms.