LI Yue.A Hybrid DL-WYL Conjugate Gradient Method[J].Journal of Chongqing Technology and Business University(Natural Science Edition）,2021,38(2):28-34

A Hybrid DL-WYL Conjugate Gradient Method

DOI：

 作者 单位 李月 重庆师范大学 数学科学学院，重庆 401331

共轭梯度法因为其迭代简单和低存储等特点,在工程问题、金融模型等许多实际领域中得到广泛的应用；针对大规模无约束优化问题,提出了一类混合的DL-WYL共轭梯度法——LHSDL方法，它可以看作是一类修正的DL共轭梯度法,即利用一个数值效果和理论结果均良好的Wei-Yao-Liu型共轭梯度法的共轭参数去修正DL共轭梯度法的第一项；它也可以看作是一类修正的WYL共轭梯度法,通过添加DL共轭梯度法的第二项,使该方法可能含有一些Hessian信息。LHSDL方法相对于DL方法具有一个较好的性质,即在强Wolfe线搜索条件下具有充分下降性，并且理论证明了LHSDL方法对于一般函数具有全局收敛性；数值实验是在CUTEr集的一组无约束优化测试问题上进行的,由Dolan和Moré的性能曲线图表明:LHSDL方法略优于DK+方法和MNVHS方法。

Conjugate gradient method is widely used in many practical fields such as engineering problems，financial models and so on because of its simple iteration and low storage.For the large scale unconstrained optimization problems，a hybrid DL WYL conjugate gradient method is proposed—LHSDL method.It can be regarded as a modified DL conjugate gradient method，the first term of DL conjugate gradient method is modified by the conjugate parameter of Wei Yao Liu type conjugate gradient method which has good numerical and theoretical results.It can also be regarded as a modified WYL conjugate gradient method.By adding the second term of DL conjugate gradient method，the method may contain some Hessian information.The LHSDL method has a better property than DL method，i.e.，under the condition of strong Wolfe line search，it has sufficient descent property，and it is theoretically proved that LHSDL method has global convergence for general functions.Numerical experiments are carried out on a set of unconstrained optimization test problems of CUTEr collection.The performance profile of Dolan and Moré shows that LHSDL method is slightly superior to DK+method and MNVHS method.