采用增广拉格朗日乘子形式的罚函数作线性搜索的递归等式约束二次逼近算法

1.引言 本文所讨论的问题如下: Min f(x) x∈R~n, s.t. c_i(x)=0,i=1,…,q,(1.1) c_i(x)≤0,i=q+1,…,p.解此问题的递归等式约束二次逼近算法,是由Murry(1969)提出,而后由Biggs(1972)发展的.此项研究是从罚函数的轨迹出发,建立一个只包含等式约束的二次规划子问题,从而可用代数的方法求得搜索方向.并沿该方向作线性搜索而完成一次迭代过程.Biggs将二次罚函数作为效应函数用于线性搜索,并证明了该算法具有全局收敛性和局部超线

A RECURSIVE EQUALITY CONSTRAINED QUADRATIC APPROXIMATION METHOD WITH AN AUGMENTED LAGRANGIAN TYPE PENALTY FUNCTION FOR LINE SEARCH

The recursive cquality constrained quadratic programming method requires least executioncomputer time for solving the constrained optimization problem. Biggs used the quadraticpenalty function for the line search and proved that the method is globally convergent.Tofurther raise the efficiency and reduce the sensitivity to some parameters, this paper presentsan augmented Lagrangian type penalty function for the line search. An algorithm is describedand the global convergence of the method is proved. Some computing results of the algorithmare showed to contrast with other algorithms of the same type.