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基于增广Lagrange函数的RQP方法
引用本文:王秀国,薛毅.基于增广Lagrange函数的RQP方法[J].计算数学,2003,25(4):393-406.
作者姓名:王秀国  薛毅
作者单位: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
基金项目:国家自然科学基金(19971008)
摘    要:Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented 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 toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, 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
修稿时间:2000年11月18

RECURSIVE QUADRATIC PROGRAMMING METHODS BASED ON THE AUGMENTED LAGRANGIAN
Wang Xiuguo School of Economics and Management,BeiHang University,Beijing, Xue Yi College of Applied Science,Beijing University of Technology,Beijing.RECURSIVE QUADRATIC PROGRAMMING METHODS BASED ON THE AUGMENTED LAGRANGIAN[J].Mathematica Numerica Sinica,2003,25(4):393-406.
Authors:Wang Xiuguo School of Economics and Management  BeiHang University  Beijing  Xue Yi College of Applied Science  Beijing University of Technology  Beijing
Institution:Wang Xiuguo School of Economics and Management, BeiHang University, Beijing, 100083) Xue Yi College of Applied Science, Beijing University of Technology, Beijing, 100022
Abstract: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.
Keywords:RQP methods  constrained optimization problem  exact penalty function  global convergence  superlinear convergence    
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