一种求解无约束优化问题的共轭梯度法

A Mixed Conjugate Gradient Method for Unconstrained Optimization

共轭梯度法是求解大规模无约束问题的一种有效方法,本文针对算法的优劣主要依赖于步长因子和搜索方向的特点,结合共轭梯度法的共轭性质,在HS方法和DY方法的基础上,提出了一种混合共轭梯度法,并证明了全局收敛性.

Conjugate gradient method is an efficient method in solving problems with unconstrained optimization, which is especially efficient in dealing with large dimension. In light of the conjugate character of conjugate gradient method and the fact that the strength or weakness of an algorithm is more or less determined by the step size and the search direction of the algorithm, a mixed conjugate gradient method is proposed based on Hestenes-stiefel Algorithms and Dai-yuan Algorithms in this paper. We prove it can ensure the convergence under a new line search.