Abstract:

In this paper, we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem. For this purpose, we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value. Then, Newton’s method is applied to find the root. The convergence of the proposed method is established under some suitable conditions. Based on the main idea of the cross-entropy method to update the sampling density function, an important sampling technique is proposed in the implementation. Preliminary numerical experiments indicate the validity of the proposed method.

Key words: Global optimization ·, Level-value estimation ·, Generalized variance function ·, Cross-entropy method