解约束优化问题的QP-free方法及其全局收敛性

A New Globally and Superlinearly Convergent QP-Free Method for Inequality Constrained Optimization

对于约束优化问题,基于Fischer-Burmeister NCP函数提出了一类新的QP-free方法.为了避免Maratos效应,引入了一个高阶修正方向.同时,算法采用线搜索以代替弧搜索.与其他传统的SQP方法不同,这个方法只需要在每步迭代中求解不多于三个线性系统的方程组,并且具有总体收敛性.在不需要假设聚点是孤立点的情况下,证明了序列的每个聚点都是优化问题的KKT点.

Based on a non-smooth equation of KKT optimality condition, this paper presents a new QPfree method for inequality constrained optimization by using the Fischer-Burmeister NCP function, which ensures the feasibility of all iterates and makes it unnecessary to search along an arc. To avoid Maratos effect, a high-order modified correction is introduced. Compared with the traditional SQP method, this new method only needs to solve no more than three systems of linear equation per iteration with global convergence and local superlinear convergence under some reachable conditions. Without assuming isolateness of the accumulation point or boundedness of the Lagrangian multiplier approximation sequence, every accumulation point of the iterative sequence generated by this method is a KKT point.