序列线性方程组方法解约束SC^1函数最小化问题

Sequential System of Linear Equations Method for Constrained Minimization of SC^1 Functions

对不等式约束SC1函数最小化问题提出一个可行的序列线性方程组算法.算法的每步迭代,子问题只需解具有相同的系数矩阵的四个简化的线性方程组.这个算法的特点是产生的迭代点是可行的;只考虑指标在集合I的一个子集Ak中的约束函数;不需假定聚点的孤立性,就可证明算法产生的迭代点全局收敛到问题的KKT(库恩-塔克)点.在较弱条件下,证明算法是超线性收敛的.

The paper first presents the problem of minimizing an SC1 function subject to inequality constraints. A feasible sequential system of linear equations algorithm is proposed to sovle the problem. At each iteration of the proposed algorithm, the subproblem consists of four reduced systems of linear e- quations with a common coefficient matrix. The distinguished features of this algorithm are that： all iterate are feasible;only constraints indexed by some subset Ak of I are considered; without assumption of the isolatedness of the stationary points, the sequence generated by the proposed algorithm proves convergent on a KKT point of the problem globally. Under some additional conditions, the convergence rate proves superlinear.