一种新的MBFGS算法

A New MBFGS Algorithm

本文在MBFGS算法的研究基础上,对该算法进行推广,形成了一种新的MBFGS算法。同时,研究了其全局收敛性并给出相关证明。一些数值实验表明,这种改进的MBFGS方法对于给定的测试问题是有效的。对于一些无约束优化问题,新的MBFGS算法平均比单调或传统的非单调格式的BFGS方法使用更少的函数和梯度求值。

Based on the research of MBFGS algorithm, this algorithm is extended to form a new MBFGS algo-rithm. At the same time, its convergence is studied and the relevant proof is given. Some numerical experiments show that the improved MBFGS method is effective for a given test problem. For some unconstrained op-timization problems, the new MBFGS algorithm uses less function and gradient evaluation than the mono-tone or traditional non monotone BFGS method.