无约束优化问题线搜索方法的收敛性

Convergence of Line Search Methods for Unconstrained Optimization

在较弱条件下给出了5种线搜索准则下的线搜索方法的收敛结论,这些结论对于构造快速有效的收敛算法是十分有用的。表明了搜索方向在这些方法中起主要作用,同时步长在一定条件下保证了算法的全局收敛性。说明了算法可用于求解更广泛的无约束优化问题。

Line search methods are traditional and successful methods for unconstrained optimization problems. Its convergence has attracted more attentions in recent years. In this paper, we analyze the general results on convergence of line search methods with five line search rules. It is clarified that the search direction plays a key role in these methods and that step-size guarantees the global convergence in some cases. We obtain the same convergence results under some weaker conditions. These convergence results can make us design powerful, effective, and stable algorithms to solve much more unconstrained optimization problems.