论文标题
使用多点对称割线矩阵改变形状变化的信任区域方法
Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices
论文作者
论文摘要
在这项工作中，我们考虑了无限制优化的大规模和非凸的方法。我们提出了一种新的信任区域方法，其子问题是使用所谓的“变形”规范以及密集至定义的多点对称secant（MSS）矩阵来定义的，以近似Hessian。改变形状的规范和密集的初始化已在传统的准牛顿方法的背景下成功使用，但在MSS方法的情况下尚未探索。数值结果表明，使用密集的MSS矩阵以及变化的规范的信任区域方法与其他信任区域方法都优于MSS。
In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi-Newton methods, but have yet to be explored in the case of MSS methods. Numerical results suggest that trust-region methods that use densely-initialized MSS matrices together with shape-changing norms outperform MSS with other trust-region methods.
