Abstract: In this paper, we propose a K-means clustering-based integral level-value estimation algorithm tosolveakindof box-constrainedglobal optimizationproblem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton's method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.

Key words: Global optimization, Generalized variance function, Multiple importance sampling, K-means clustering algorithm