| 一类逼近l1精确罚函数的罚函数 |
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| 引用本文： | 连淑君,刘丙状,张连生.一类逼近l1精确罚函数的罚函数[J].应用数学学报,2007,30(6):961-971. |
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| 作者姓名： | 连淑君 刘丙状 张连生 |
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| 作者单位： | 1. 曲阜师范大学运筹与管理学院,曲阜,273165;上海大学数学系,上海,200444
2. 上海大学数学系,上海,200444 |
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| 基金项目： | 国家自然科学基金;曲阜师范大学校科研和教改项目 |
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| 摘 要： | 本文对可微非线性规划问题提出了一个渐近算法,它是基于一类逼近l1精确罚函数的罚函数而提出的,我们证明了算法所得的极小点列的聚点均为原问题的最优解,并在Mangasarian-Fromovitz约束条件下,证明了有限次迭代之后,所有迭代均为可行的,即迭代所得的极小点为可行点.
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| 关 键 词： | 可行点 罚函数 精确罚函数 Mangasarian-Fromovitz约束条件 |
| 收稿时间： | 2006-12-26 |
| 修稿时间： | 2007-09-24 |
A Family of Penalty Functions Approximate to l1 Exact Penalty Function |
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| LIAN SHUJUN,LIU BINGZHUANG,ZHANG LIANSHENG.A Family of Penalty Functions Approximate to l1 Exact Penalty Function[J].Acta Mathematicae Applicatae Sinica,2007,30(6):961-971. |
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| Authors: | LIAN SHUJUN LIU BINGZHUANG ZHANG LIANSHENG |
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| Abstract: | In this paper, we study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function for the differentiable nonlinear programming problem. We prove that the minimizer sequence generated by the algorithm is bounded, and its accumulation points are optimal solutions of primal problem. We show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. |
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| Keywords: | feasible point penalty function exact penalty function Mangasarian-Promovitz constraint qualification |
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