基于有效约束识别技术的一个SSLE算法及其收敛性分析

基于一个有效约束识别技术, 给出了具有不等式约束的非线性最优化问题的一个可行SSLE算法. 为获得搜索方向算法的每步迭代只需解两个或三个具有相同系数矩阵的线性方程组. 在一定的条件下, 算法全局收敛到问题的一个KKT点. 没有严格互补条件, 在比强二阶充分条件弱的条件下算法具有超线性收敛速度.

An Active Constraints Identification Technique-based SSLE Algorithm and Its Convergence Analysis

In this paper,based on an active set identification technique,a new feasible se- quential system of linear equations (SSLE) algorithm is proposed for nonlinear optimization problems with inequality constraints.At each iteration,only two or three systems of linear equations with a common coefficient matrix are solved to obtain the search direction.Under mild conditions,the suggested algorithm converges globally to a KKT point of the problem. Without assuming the strict complementarity,the convergence rate is proved to be superlinear under a condition weaker than the strong second-order sufficiency condition.