论文标题
BobyQA的HERMITE型修改以优化一些部分衍生物
Hermite-type modifications of BOBYQA for optimization with some partial derivatives
论文作者
论文摘要
在这项工作中，我们提出了两种HERMITE型优化方法，Hermite最小二乘和Hermite Bobyqa，专门针对目标功能的某些部分衍生物，而另一些则没有。主要目的是通过保持收敛属性来减少目标函数调用的数量。两种方法都是对Powell无衍生物BobyQA算法的修改。但是，训练数据并没有（如果不确定的）插值来构建二次子问题，而是训练数据富含第一阶衍生物，然后使用（加权）最小二乘回归。讨论了全局收敛的证明，并提供了数值结果。此外，在收益优化的背景下，对现实的测试案例进行了适用性。数值测试表明，如果有一半或更多的部分衍生物可用，则HERMITE最小二乘接近经典的Bobyqa。此外，在嘈杂的目标函数的情况下，Hermite类型的方法实现了更强的鲁棒性，从而获得了更好的性能。
In this work we propose two Hermite-type optimization methods, Hermite least squares and Hermite BOBYQA, specialized for the case that some partial derivatives of the objective function are available and others are not. The main objective is to reduce the number of objective function calls by maintaining the convergence properties. Both methods are modifications of Powell's derivative-free BOBYQA algorithm. But instead of (underdetermined) interpolation for building the quadratic subproblem in each iteration, the training data is enriched with first and -- if possible -- second order derivatives and then (weighted) least squares regression is used. Proofs for global convergence are discussed and numerical results are presented. Further, the applicability is verified for a realistic test case in the context of yield optimization. Numerical tests show that the Hermite least squares approach outperforms classic BOBYQA if half or more partial derivatives are available. In addition, the Hermite-type approaches achieve more robustness and thus better performance in case of noisy objective functions.
