求解无约束优化的新子空间共轭梯度法

A New Subspace Conjugate Gradient Method for Solving Unconstrained Optimization

通过引入惩罚参数平衡下降性和共轭性,在二维子空间上建立一种新的优化模型,然后极小化该模型导出具有充分下降性的搜索方向,结合重启技术,提出新的子空间共轭梯度算法,在适当假设条件下证明了算法的全局收敛性,数值实验表明新算法是有效的.

A new optimization model is established on the two-dimensional subspace by introducing penalty parameters to balance the descent and conjugation.The new search direction with sufficient descent is derived by minimizing this model.Combining the restart technique,we proposed a new subspace conjugate gradient algorithm.The global convergence of new algorithm is proved under appropriate assumptions,numerical experiments showed that new algorithm is effective.