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

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.