一种多参数谱三项共轭梯度法

A multi-parameter spectral three-terms conjugate gradient method

通过求解带有罚参数的优化问题设计共轭梯度法是一种新思路.基于Fatemi的优化问题求解,通过估计步长和选择合适的罚参数建立一个谱三项共轭梯度法,为证得算法的全局收敛性对谱参数进行修正.在标准Wolfe线搜索下证明了该谱三项共轭梯度算法的充分下降性以及全局收敛性.最后,在选取相同算例的多个算法测试结果中表明新方法数值试验性能表现良好.

It is a new idea to design conjugate gradient method by solving optimization prob-lems with penalty parameters.Based on the optimization problem of Fatemi,a spectral three-terms conjugate gradient method is established by estimating step size and selecting appropriate penalty parameters,and the spectral parameters are modied to prove global convergence.Then,the sufficient descent and global convergence of the multi-parameter spectral three-terms conjugate gradient algorithm are proved under the standard Wolfe line search.Finally,the new method performs well in numerical experiments among several test algorithms with the same examples.