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