This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large....This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large. We demonstrate that by properly varying the noise intensity, approximations to the global maximum can be achieved. We also show that the expected time to reach the domain of attraction of the global maximum, which can be approximated by the solution of a boundary value problem, is finite. Discrete-time algorithms are proposed; recursive algorithms with occasional perturbations involving large noise intensity are developed. Numerical examples are provided for illustration.展开更多
基金Supported by the National Science Foundation under grants DMS-0304928 and CMS-0510655,the National Natural Science Foundation of China(No.60574069)the U.S.Department of Agriculture,Minnesota Agricultural Experiment Stations
文摘This work develops an algorithm for global optimization. The algorithm is of gradient ascent type and uses random perturbations. In contrast to the annealing type procedures, the perturbation noise intensity is large. We demonstrate that by properly varying the noise intensity, approximations to the global maximum can be achieved. We also show that the expected time to reach the domain of attraction of the global maximum, which can be approximated by the solution of a boundary value problem, is finite. Discrete-time algorithms are proposed; recursive algorithms with occasional perturbations involving large noise intensity are developed. Numerical examples are provided for illustration.
