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运筹学学报 ›› 2012, Vol. 16 ›› Issue (1): 56-66.

• 运筹学 • 上一篇    下一篇

一种新的逼近精确罚函数的罚函数及性质

尚有林1, 刘牧华1,  李璞1   

  1. 1. 河南科技大学数学与统计学院, 河南洛阳， 471003
  • 收稿日期:2011-04-02 修回日期:2011-12-26 出版日期:2012-03-15 发布日期:2012-03-15
  • 通讯作者: 尚有林

A New Penalty Function Based on Non-coercive Penalty Functions

   Shang-You-Lin1, LIU  Mu-Hua1, LI  Pu1   

  1. 1. School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471003, China
  • Received:2011-04-02 Revised:2011-12-26 Online:2012-03-15 Published:2012-03-15
  • Supported by:

    The work is partially supported by The National Natural Science Foundation of China (No.10971053, 10771162), and  The National Natural Science Foundation of Henan (No. 094300510050).

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1511

被引次数

6

摘要： 针对可微非线性规划问题提出了一个新的逼近精确罚函数的罚函数形式，给出了近似逼近算法与渐进算法，并证明了近似算法所得序列若有聚点，则必为原问题最优解. 在较弱的假设条件下，证明了算法所得的极小点列有界，且其聚点均为原问题的最优解，并得到在Mangasarian-Fromovitz约束条件下，经过有限次迭代所得的极小点为可行点.    

关键词:  精确罚函数, 可行点, 最优解, 非线性规划

Abstract: For the differentiable nonlinear programming problem, this paper proposes a new penalty function form of the approached  exact penalty function, presents
 with the gradual  approximation algorithm and evolutionary algorithm, and proves   that if the sequences of the approximation algorithm   exist accumulation point, it certainly is the optimal solution of original problem. In the weak assumptions,    we prove that the minimum sequences from the algorithm is bounded, and its accumulation points are the optimal    solution of the original problem and get that in the Mangasarian-Fromovitz qualification condition, through     limited iterations the minimum point is the feasible point.

Key words:  exact penalty function, the feasible point, optimal solution, nonlinear programming