非线性最优化楔形信赖域算法的改进.pdfVIP

摘 要 摘 要 楔形信赖域算法是基于传统的信赖域算法提出的，主要用于求解无导数的优化问 题。楔形信赖域算法的改进之处是在传统的信赖域子问题的基础上增加一个楔形约束， 故称为“楔形信赖域”。另外，信赖域半径的更新方法对于算法的收敛性有重要的影响。 本文针对原楔形信赖域的半径更新方法的不足，分别从二次模型和线性模型的角度改进 该算法。对于二次模型，我们提出了一种半径更新的方法；同时，我们提出了两种针对 线性模型的更新半径的方法。实验结果表明，在大多数测试问题上，改进的这三种算法 的函数值计算次数都有很大下降。 最后，我们考虑将两种模型结合起来求解无导数优化问题。在算法的初始阶段使 用线性模型，若满足一定条件则转到二次模型；否则继续使用线性模型直到算法终止。 同时，我们将改进的楔形信赖域算法与基于单一模型的算法进行比较。实验结果表明， 混合模型的楔形信赖域算法优于传统单一模型的算法，并且在多数问题上是比较有效 的。 关键词 直接有哪些信誉好的足球投注网站法 楔形信赖域 无约束优化 无导数优化 半径的更新 线性模型 二次模型 I Abstract Abstract Wedge trust region method based on traditional trust region is designed for derivative free optimization problems. The novelty of wedge trust region is to add a constraint to the trust region subproblem, which is called “wedge trust region”. In addition, the radius update rules have a strong influence on the performance of an algorithm. In this paper, faced with the disadvantages of the original radius update rule, we improve the algorithm from the angle of quadratic and linear models respectively. When choosing the quadratic models, we propose a method for updating radius; at the same time, we also proposed two methods for linear models to update the radius. For most test problems, the experiments demonstrate the numbers of function evaluations of the three methods are both reduced significantly compared with the former one. Finally, we consider combining the two versions of models to solve the derivative free optimization problems. We would choose linear models in the initial stages of our algorithm. If some certain conditions are satisfied we will use