Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (1): 56-66.

• Original Articles • Previous Articles     Next Articles

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).

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