约束变尺度类算法(Ⅱ)——两步超线性收敛的广义投影梯度约束变尺度方向类

CONSTRAINED VARIABLE TYPE METHODS(Ⅱ) ——The generalized projection gradient type algorithm with superlinear convergence

将Ｈａｎ－Ｐｏｗｅｌ和文献［１］中算法的思想有机的结合在一起，构造了广义投影梯度约束变尺度方向所满足的线性系统．从而建立了具有两步超线性收敛的广义投影梯度约束变尺度类算法Ｃ．该算法为统一算法模型Ａ提供了一个重要的子类．到此，统一算法模型Ａ已包括了Ｈａｎ－Ｐｏｗｅｌ算法和既约梯度、投影梯度型、广义投影梯度型约束变尺度类算法．从而形成了一个丰富的理论算法库．与此同时，这些算法也被自然的推广到非单调一维搜索的情形．

Combining the idea of Han Powell′s algorithm with that of the algorithm in,the linear system satisfied by constrained variable directions with generalized projection gradient is proposed.On the basis the constrained variable algorithm model C with generalized projection gradient is presented.The model gives an important subclass of unified algorithm model A.Thus the model A contains Han Powell's algorithm and the class of constrained variable methods with reduced gradient,projected gradient and generalized projection gradient,and a rich base of theoretical algorithms is formed.These algorithms can also be extended to the those with nonmonotone search.