解带线性或非线性约束最优化问题的结合共轭梯度参数的记忆梯度Rosen投影算法

对于求解无约束规划的记忆梯度算法中的参数。作者利用Rosen投影矩阵给出了一个条件以确定其取值范围。使其在取值范围内取值均能得到目标函数的记忆梯度Rosen投影下降方向。从而建立了求解带线性或非线性约束最优化问题的记忆梯度Rosen投影算法．然后在较弱条件下证明了算法的收敛性。同时给出了具有好的收敛性质和较快收敛速度的结合FR，PR，HS共轭梯度参数的记忆梯度Rosen投影算法，从而将经典的共轭梯度法推广用于求解约束规划问题．由于算法需要较小的存储，算法适合于大规模问题的计算．数值例子表明算法是有效的．

Memory Gradient Rosen Projection Method with Conjugate Gradient Scalar for Nonlinear Programming with Linear or Nonlinear Inequality Constraints

By using Rosen projection matrix, conditions are given on the scalars in memory gradient direction to ensrure that the memory gradient projection direction is descent. A new memory gradient Rosen projection method for nonlinear programming with linear or nonlinear inequality constraints is presented.The global convergence properties of the new method are discussed. Combining with conjugate gradient scalar with this new method,three new classes (FR,PR,HS) of memory gradient Rosen projection methods with conjugate gradient scalar are presented. The new methods use little storage,thus the methods are attractive for large?scale problems. The numerical results show that the new methods are effective.