关于Powell猜想的探讨

On the Investigation of Powell’s Conjecture

变尺度算法的研究一直是无约束最优化的一个热点，而ＤＦＰ算法是出现得最早的一种变尺度算法，有关它的收敛性研究以Ｐｏｗｅｌｌ的一系列开创性结果为标志，然而，对于非凸函数带精确搜索的ＤＦＰ算法是否具有全局收敛性，一直是一个公开的难题，即Ｐｏｗｅｌｌ猜想。本文给出一组假设条件（Ｈ），在此条件下，Ｐｏｗｅｌｌ猜想正确。

The research of variable metric algorithms has been being one of the focus of interests inunconstrained optimization,it is well-known that DFP algorithm is the earliest variable met-ric algorithm,the research in its convergence is shown by a series of Powell’s Pioneering re-sults。However,for nonconvex functions , it has still been an open problem whether the DFPalgorithm with exact linesearch is globally convergent,this is well-known Powell’s conjec-ture。 In this paper, we give a assumption(H),under this assumption we prove that Powell’sconjecture holds。