非线性最优化一个超线收敛的可行下降算法

A SUPERLINEARLY CONVERGENT FEASIBLE DESCENT ALGORITHM FOR NONLINEAR OPTIMIZATION

本文讨论非线性等式和不等式约束最优化的求解方法。首先将原问题扩充成一个只含不等式约束的参数规划，对于充分大的参数，扩充问题与原问题是等价的。然后建立具有以下特点的一个新算法。１）算法对扩充问题而言是可行下降的，参数只须自动地调整有限次；２）每次迭代仅需解一个二次规划；３）在适当的假设下，算法超线性收敛于原问题的最优解。

This paper discusses optimization with nonlinear equality and inequality cnstrainets.First the original problems are expanded to parametric programming problems halding only nequality constraints,and the expansive problems are equivalent to the original problems if the parameter is large enough.Then a new algorithm possessing following properties is pre-sented.1 The algorithm is a feasible descent method for the expansive problems,and the. parameter adjusts automatically only for finit times;2)Only one quadratic programming need to be solved at each iteration;3)It superlinearly converges to the solution for original prblem under some suitable assumptions.