【摘要】 <正> 全局收敛性是最优化算法应具备的一个基本性质,研究各种最优化算法的全局收敛性是非线性规划的一个重要理论问题.Zangwill 借助点到集映象来构成抽象算法这一研究途径,分析和综合了各种具体最优化算法的收敛特征,并且利用闭映象的概念提出了抽象算法的收敛条件,而后这方面的工作得到了广泛重视而有了很大的发展.Polak,Meyer,Huard,Denel,Yue 等人,都发展了 Zangwill 的研究工作.他们分别提出了多种抽象算法模型,并且研究了它们的收敛性.这些理论结果对具体算法的研究中有了重要和广泛的应用.更多还原

【Abstract】 Zangwill is the first who described optimization algorithms by introducing point-to-setmaps,thanks to which he has also established a unified approach to convergence study.Con-sequently,various concept algorithm models and corresponding convergence conditions areproposed.This paper gives a set of new conditions for optimization algorithms with monoto-nic property;still more it is proved that the newly-proposed conditions are weaker thanmany existing ones.Finally,it is demonstrated that Rosen’s method is convergent by justifyingthat it satisfies new conditions.更多还原