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| 序列线性方程组方法解约束SC1函数最小化问题 | |
| 引用本文： | 周岩,桂胜华,濮定国.序列线性方程组方法解约束SC1函数最小化问题[J].同济大学学报(自然科学版),2007,35(9):1269-1273. |
| 作者姓名： | 周岩 桂胜华 濮定国 |
| 作者单位： | 1. 同济大学,数学系,上海,200092;青岛大学,管理科学与工程系,山东,青岛,266071 2. 上海第二工业大学,应用数学系,上海,201029 3. 同济大学,数学系,上海,200092 |
| 摘 要： | 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. |
| 关 键 词： | 不等式约束优化 序列线性方程组算法 全局收敛性 |
| 文章编号： | 0253-374X（2007）09-1269-05 |
| 修稿时间： | 2005-12-20 |
Sequential System of Linear Equations Method for Constrained Minimization of SC1 Functions |
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| ZHOU Yan,GUI Shenghua,PU Dingguo.Sequential System of Linear Equations Method for Constrained Minimization of SC1 Functions[J].Journal of Tongji University(Natural Science),2007,35(9):1269-1273. | |
| Authors: | ZHOU Yan GUI Shenghua PU Dingguo |
| Institution: | 1. Department of Mathematics, Tongji University, Shanghai 200092, China; 2. Department of Management Science and Engineering, Qingdao University, Qingdao 266071, China; 3. Department of Applied Mathematics, Shanghai Second Polytechnic University, Shanghai 201209, China |
| Abstract: | 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 equations 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. |
| Keywords: | inequality constrained optimization sequential system of linear equations method global convergence |
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