Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (2): 105-114.

• Original Articles • Previous Articles     Next Articles

A new level-value estimation method for  global minimization

   Lou-Ye1,2, SUN  Sheng2, WU  Ming-Nan2   

  1. 1. Shanghai Vocational College of Science and Technology, Shanghai 201800, China; 2. School of Sciences, Shanghai University, Shanghai 200444, China
  • Online:2012-06-15 Published:2012-06-15

Abstract: In this paper, a new level-value estimation method is proposed for solving global optimization problem. For this purpose,  we introduce a deviation function and study its properties.  Based the deviation function, we give a global optimality condition, and then propose a conceptual level-value estimation algorithm, and prove the global convergence of the proposed method.  For the implementation of the proposed method, we use the Monte-Carlo method with important sampling to compute the deviation, in which the sample density is updated by the main ideas of the cross-entropy method.  Some primary numerical
results show the validity of the proposed method.

Key words: global optimization, deviation function, the level-value estimation, important sampling, the cross-entropy method