对支撑集搜索法约定的一些标注

实际工程应用的很多非线性规划(NLP)模型都是非光滑问题,传统优化技术如拟牛顿法或最速下降法无法很好地求解这些问题.不依赖于方向导数计算或逼近的直接搜索法(Direct Searches)或支撑集搜索法GSS(Generating Set Searches)在近几年来得到较多的关注和研究.本文对GSS约定的一些要求,如充分下降和简单下降条件对步长接受准则的影响,如何避免较差的下降方向和迭代步长,为什么必须给定步长收缩因子的上界等进行标注,以便为该领域的进一步深入研究提供参考.

Some notes on the specifications in generating set searches

Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice, direct searches or generating set searches (GSS) that need no recourse to explicit derivatives are revived and become popular again. Some notes on the requirements of the specifications in generating set searches, such as sufficient decrease vs. simple decrease in step acceptance criteria, how to prevent poor choices of too long or too short step lengths, how to avoid poor descent directions, why need an upper bound on the contraction parameter, etc., are made in this paper, in order to provide some background materials for people who want to get a deep insight into this field.