一种新的非单调谱共轭梯度算法

A New Nonmonotone Spectral Conjugate Gradient Algorithm

提出了一类新的非单调谱共轭梯度方法.该方法通过引入混合因子,将HS方法和PRP方法结合得到共轭系数的新的选取方式.以此为基础,通过合适地选取谱系数保证了所有搜索方向不依赖于线搜索条件,恒为充分下降方向.其次,该方法还修正了Zhang和Hager提出的非单调线搜索规则,在更弱的假设条件下证明了全局收敛性.数值试验说明了该方法的计算性能优良.

In this paper, a new spectral conjugate gradient method is proposed. By introducing a hybrid coefficient, the conjugacy parameter is determined based on the combination of PRP and HS methods. Then, a spectral parameter is appropriately chosen such that each search direction is a sufficiently descent direction independent of the employed line search techniques. On the other hand, the nonmonotone line search technique proposed by Zhang and Hager is modified, and under more mild assumptions, the global convergence of the developed algorithm is proved. Numerical experiments are employed to demonstrate the efficiency of the algorithm.