一个基于近似下降方向的免梯度算法

A Derivative-free Algorithm Based on Approximate Descent Direction

本文构造一个求解非线性无约束优化问题的免梯度算法,该算法基于传统的模矢法,每次不成功迭代后,充分利用已有迭代点的信息,构造近似下降方向,产生新的迭代点。在较弱条件下,算法是总体收敛的。通过数值实验与传统模矢法相比,计算量明显减少。

This paper presents an accelerated derivative-free algorithm for unconstrainged optimization, which is based on traditional pattern search method. After an unsuccessful iterate, it makes full use of the information of the existing iterates to construct an approximate descent direction in order to get a new iterate point. Under weaker conditions, the algorithm is globally convergent.The numerical experiment shows that the algorithm is better than the traditional pattern search method in the aspect of calculating quantity.