无导数最优化中的模式搜索算法研究

发布时间：2018-04-06 23:16

本文选题：无约束最优化　切入点：无导数方法　出处：《河北大学》2015年硕士论文

【摘要】：模式搜索算法属于最优化领域中的无导数优化范畴,是针对最优化问题中目标函数无导数信息可以利用而设计的只利用函数值信息的算法。模式搜索算法的特点是直观,简洁,是其它优化算法失效时优先考虑的算法。其缺点是由于算法设计只利用目标函数的函数值信息,无法利用有效的函数曲率信息,而导致大多数同类算法的运行效率较慢。为了使模式搜索算法得到更快的收敛速度,更好的数值结果,基于经典的模式搜索以及子空间技巧,本文引入了一个参数M,通过控制成功迭代以后的延伸搜索,充分利用当前迭代点附近的下降信息。使算法尽可能的利用已经获得的局部信息。具体是在找到的下降方向上为了得到更好的解我们最多进行M步搜索。我们测试了不同的数值,实验数据证明当M?2时,算法效果最好。本文的第二部分工作是将上述方法推广到简单有界约束的最优化问题,同样利用子空间搜索技巧,提出了一种改进的无导数最优化算法,具体是算法不在同一方向上进行充分搜索,而是当算法在当前迭代点搜寻两个不同的下降方向,然后对这两个方向进行复合,形成搜索子空间,然后在复合方向上利用延伸压缩等技巧进行搜索。最后,本文根据算法进行了大量的数值实验,结果表明,我们提出的改进算法具有较高的运算效率。
[Abstract]:The pattern search algorithm belongs to the category of non-derivative optimization in the field of optimization. It is designed to use only the information of function value for the purpose function of optimization problem without derivative information can be used.The characteristic of pattern search algorithm is intuitive and concise, which is the priority algorithm when other optimization algorithms fail.Its shortcoming is that the algorithm design only uses the function value information of the objective function, but cannot use the effective function curvature information, which results in the slow running efficiency of most similar algorithms.In order to obtain faster convergence speed and better numerical results for pattern search algorithm, based on classical pattern search and subspace technique, a parameter M is introduced in this paper.Make full use of the descent information near the current iteration point.Make the algorithm make use of the local information as much as possible.In order to get a better solution, we do M step search at most.We have tested different numerical values, and the experimental data show that the algorithm is the best when M? 2 is used.The second part of this paper is to extend the above method to the simple bounded constrained optimization problem. In the same way, by using the subspace search technique, an improved derivative free optimization algorithm is proposed.In particular, the algorithm does not search fully in the same direction, but when the algorithm searches for two different descent directions at the current iteration point, the two directions are combined to form a search subspace.Then search in the compound direction using techniques such as extension compression.Finally, a large number of numerical experiments are carried out according to the algorithm, and the results show that the improved algorithm has high computational efficiency.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O224

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