Accelerations for global optimization methods that use second derivative information

摘要

Two new improvements for the algorithm of Breiman & Cutler are presented. Better envelopes can be built up using positive definite quadratic forms. Better utilization of first and second derivative information is attained by combining both global aspects of curvature and local aspects nearthe global optimum. The basis of the results is the geometric viewpoint developed by the first author and can be applied to a number of covering type methods. Improvements in convergence rates are demonstrated empirically on standard test functions.