Newton-PCG算法的数值性态

Numerical experiences with Newton-PCG method

理论上,Newton-PCG算法适于求解大规模无约束优化问题,并且牛顿 预优最速下降法优于Newton-PCG算法。在实际应用中,Newton-PCG算法是否有效需经过大量数值试验验证。通过数值试验得出:在维数相同的情况下,Newton-PCG算法比牛顿 预优最速下降法求解时间短。表明Newton-PCG算法优于牛顿 预优最速下降法,比率与问题的维数并无太大关系。

Theoretically Newton-PCG method is fit for large scale unconstrained optimization problems, and it is less efficient than the Newton preconditioned maximum descent method . In practice, Newton-PCG method needs to be proved by many numerical experiments whether it is efficient or not. The run-time of Newton-PCG method is less than that of Newton preconditioned maximum descent method at the same dimension by numerical experiments. Numerical experiences show that Newton-PCG method is a little better than Newton preconditioned maximum descent method, and the ratio of the run-time has nothing to do with the problem's dimension.