一种既约逐步二次规划算法的全局收敛性  

A Reduced Successive Quadratic Programming Algorithm for Nonlinearly Equality Constrained Optimization

作　　者：王玮[1] 陈兰平[1] 焦宝聪[1] 

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《首都师范大学学报（自然科学版）》2008年第6期1-6,11,共7页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金(60472071);北京市教委科研基金(KM200710028001)资助

摘　　要：提出一种求解非线性等式约束问题的既约逐步二次规划(RSQP)算法.为避免Maratos效应,我们采用Flether的光滑精确罚函数的逼近形式作为价值函数,并且分别对Lagarange函数的单边既约Hessian的近似阵和双边既约Hessian的近似阵进行校正.在一般的条件下,证明了算法的全局收敛性并作了一定量的数值试验.In this paper,we propose a reduced successive quadratic programming algorithm for solving optimization problems with nonlinear equality constraints.In order to avoid the Maratos effect,the merit functions used are approximations to Flether＇s differentiable exact penalty function,and the algorithm updates approximations to one-sided reduced Hessian and two-sided reduced Hessian seperately.Global convergence is proved,and some numerical results are given.

关 键 词：既约逐步二次规划 既约Hessian方法 价值函数 精确罚函数 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]