学术
序列线性方程组方法解约束SC^1函数最小化问题
周岩[1,2] 桂胜华[3] 濮定国[1]
[1]同济大学数学系,上海200092 [2]青岛大学管理科学与工程系,山东青岛266071 [3]上海第二工业大学应用数学系,上海201029
摘 要:
对不等式约束SC^1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，的一个子集A^k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．[著者文摘]
文章出处:
《同济大学学报：自然科学版》-2007年35卷9期 -1269-1273页
栏目信息:
分 类 号:
文献标识码:
A
文章编号:
0253-374X（2007）09-1269-05
Sequential System of Linear Equations Method for Constrained Minimization of SC^1 Functions
ZHOU Yan, GUI Shenghua, PU Dingguo （ 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 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.[著者文摘]
Key words:
inequality constrained optimization; sequential system of linear equations method; global convergence
基金资助:
国家自然科学基金资助项目（10571137）;上海市教委科研资助项目（05RZ12）
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