初始点任意的解非线性不等式约束优化问题的结合共轭梯度参数的超记忆梯度广义投影算法  

GENERALIZED SUPER-MEMORY GRADIENT PROJECTION METHOD WITH ARBITRARY INITIAL POINT AND CONJUGATE GRADIENT SCALAR FOR NONLINEAR PROGRAMMING WITH NONLINEAR IN-EQUALITY CONSTRAINTS

作　　者：孙清滢[1] 

机构地区：[1]石油大学应用数学系,山东东营257061

出　　处：《计算数学》2004年第4期401-412,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10171055)

摘　　要：本文利用广义投影矩阵,对求解无约束规划的超记忆梯度算法中的参数给出一种新的取值范围以保证得到目标函数的超记忆梯度广义投影下降方向,并与处理任意初始点的方法技巧结合建立求解非线性不等式约束优化问题的一个初始点任意的超记忆梯度广义投影算法,在较弱条件下证明了算法的收敛性,同时给出结合FR,PR,HS共轭梯度参数的超记忆梯度广义投影算法,从而将经典的共轭梯度法推广用于求解约束规划问题,数值例子表明算法是有效的。In this paper, by using generalized projection matrix, conditions are given on the scalars in the super-memory gradient direction to ensure that the super-memory gradient projection direction is a descent direction. A generalized super-memory gradient projection method with arbitrary initial point for nonlinear programming with nonlinear in-equality constraints is presented. The global convergence properties of the new method are discussed. Combining with conjugate gradient scalar with our new method, a new class of generalized super-memory gradient projection methods with conjugate gradient scalar is presented. The numerical results illustrate that the new methods are effective.

关 键 词：广义投影 不等式约束 共轭梯度 求解 优化问题 弱条件 超记忆梯度算法 初始点 参数 非线性 

分 类 号：O241[理学—计算数学]