超线性与二次收敛序列线性方程组算法

摘要

本文,在无严格互补条件下,对非线性不等式约束最优化问题提出了一个新的序列线性方程组(简称SSLE)算法.算法有两个重要特征:首先,每次迭代,只须求解一个线性方程组或一个广义梯度投影阵,且线性方程组可以无解.其次,初始点可以任意选取.在无严格互补条件下,算法仍有全局收敛性、强收敛性、超线性收敛性及二次收敛性.文章的最后,还对算法进行了初步的数值实验.%In this paper, the nonlinear inequality constrained optimization problems without strict complementarity are discussed, and a new algorithm of sequential systems of linear equations (SSLE for short) for this problems is presented. It possesses two important characters: At each iteration, only one system of linear equations need to be solved or one generalized gradient projection need to be computed, moreover, the system of linear equations may be allowed to has no solution; its starting point is arbitrary and must not be feasible. Under w()aker assumptions without the strict comp lementarity, the algorithm is proved to possess glol()al and strong convergence, superlinear and quadratic convergence.Finally, some elementary numerical tests are reported.