带有循环策略的自适应截断BB梯度法研究

Research on Adaptive Truncated BB Gradient Method with Cyclic Strategy

考虑一般无约束优化问题,对两种修正的BB步长(Barzilai-Borwein步长)采用凸组合形式,对凸组合参数采取循环使用步长的策略推导一个新步长,结合Zhang-Hager非单调线搜索技术设计了一种自适应截断BB梯度算法——ATMBB算法。在适当的假设下,ATMBB算法是全局收敛的,目标函数为强凸函数时,该算法具有线性收敛速度,数值试验表明,此方法是有效的。

Considering the general unconstrained optimization problem,the study adopts convex combination form for two modified BB steps(Barzilai-Borwein steps);derives a new step size for convex combination parameters with cyclic step size strategy;designs an adaptive truncated BB gradient algorithmb based on Zhang-Hager non-monotonic line search technique,i.e.ATMBB algorithm.Under proper assumptions,the ATMBB algorithm is globally convergent.When the objective function is strongly convex,the algorithm has linear convergence rate.Numerical experiments show that the method is effective.