基于增广Lagrange函数的约束优化问题的一个信赖域方法

A Trust Region Method for Constrained Optimization Problems Based on Augmented Lagrange Functions

本文提出一个求解不等式约束优化问题的基于指数型增广Lagrange函数的信赖域方法.基于指数型增广Lagrange函数,将传统的增广Lagrange方法的精确求解子问题转化为一个信赖域子问题,从而减少了计算量,并建立相应的信赖域算法.在一定的假设条件下,证明了算法的全局收敛性,并给出相应经典算例的数值实验结果.

A trust region method based on exponential augmented Lagrange function for solving inequality constrained optimization problems is proposed.Based on the exponential augmented Lagrange function,the exact subproblem of the traditional augmented Lagrange method is transformed into a trust region subproblem to reduce the computational complexity.And the corresponding trust region algorithm is established.Under some assumptions,the global convergence of the algorithm is proved,and the numerical experimental results of the corresponding classical examples are given.