基于增广Lagrange函数的RQP方法  

RECURSIVE QUADRATIC PROGRAMMING METHODS BASED ON THE AUGMENTED LAGRANGIAN

作　　者：王秀国[1] 薛毅[2] 

机构地区：[1]北京航空航天大学经济管理学院,北京100083 [2]北京工业大学应用数理学院,北京100022

出　　处：《计算数学》2003年第4期393-406,共14页Mathematica Numerica Sinica

基　　金：国家自然科学基金(19971008)

摘　　要：1.引言 对于等式约束规划问题 min f(x) s.t. c(x)=0 其中f:Rn→ R,c:Rn→ Rm.Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems. This paper describes a new method for constrained optimization which obtains its search directions from a quadratic programming subproblem based on the well-known augmented Lagrangian function. It avoids the penalty parameter to tend to infinity. We employ the Fletcher's exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need to evaluate the second order derivatives of the problem functions. We prove that the algorithm possesses global and super linear convergence properties. At the same time, numerical results are reported.

关 键 词：增广LAGRANGE函数 RQP方法 精确罚函数 全局收敛性 局部超线性收敛性 等式约束规划 

分 类 号：O221[理学—运筹学与控制论]