改进的共轭梯度法及其收敛性

共轭梯度法是求解大规模无约束优化问题的一种有效方法。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，提出一种改进的可以控制步长因子的共轭梯度算法。在建立算法的几个重要引理和全局收敛性定理后分别给出了证明。最后对算法进行了数值实验，实验结果表明算法具有良好的收敛性和有效性。

Modified Conjugate Gradient Method with Global Convergence Property

Conjugate gradient method is an efficient method in solving problems with unconstrained optimization, which is especially efficient in dealing 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 modified conjugate gradient method is proposed in this paper. Some important lemmas and global convergence theorem for the new method are given and proved as follows. The numerical results suggest that the method is convergent and efficient in resolving the given test problems.