求解非线性等式约束优化问题的共轭梯度投影算法  

General Conjugate Gradient Projection Method for Nonlinear Programming with Nonlinear 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：《工程数学学报》2004年第2期217-221,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金项目(10171055).

摘　　要：利用投影矩阵,对求解无约束规划的共轭梯度算法中的参数βk给一限制条件确定βk的取值范围,以保证得到目标函数的共轭梯度投影下降方向,建立了求解非线性等式约束优化问题的共轭梯度投影算法,并证明了算法的收敛性。数值例子表明算法是有效的。By using projection matrix, conditions are given on the scalar in the conjugate gradient direction to ensure that the generalized conjugate gradient projection direction is descent, and a generalized conjugate gradient projection method for nonlinear optimization with nonlinear equality constraints is presented. The global convergence properties of the new method are discussed. The numerical results illustrate that the new methods are effective.

关 键 词：非线性规划 非线性等式约束 投影 共轭梯度 收敛 

分 类 号：O221.2[理学—运筹学与控制论]