约束变尺度类算法(Ⅰ)——统一算法模型及既约梯度型方向算法类

CONSTRAINED VARIABLE TYPE METHODS(Ⅰ)——The unified algorithm model and reduced gradient directions type algorithm

建立了非单调一维搜索约束变尺度类统一算法模型，提出收敛性条件，并证明了算法的全局收敛性．通过引入连续优势函数和Ａ－方向集的概念，将约束变尺度算法与可行方向法合二为一．不仅推广了“经典”的约束变尺度算法（可进行非单调一维搜索）．而且可得出许多新的算法，这些新算法既具有“经典”约束变尺度法“宽通路”的特征．也具有可行方向法单步计算量较小，计算程序简单的优点．进一步构造了一个方便实用的连续优势函数，并在此基础上建立了既约梯度型方向约束变尺度算法类．

A unified algorithm model of constrained variable methods(CVM) with nonmonotone search is presented and its global convergence is proved.By using the concept of continuous dominated function proposed,the CVM and feasible directions methods are unified,which extends the common CVM and can lead to many new algorithms having the advantages of both.The CVM with reduced gradient type directions is discussed.