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Numerical Experience with Multiple Update Quasi-Newton Methods for Unconstrained Optimization

机译:无约束优化的多重更新拟牛顿法的数值经验

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The authors have derived what they termed quasi-Newton multi step methods in [2]. These methods have demonstrated substantial numerical improvements over the standard single step Secant-based BFGS. Such methods use a variant of the Secant equation that the updated Hessian (or its inverse) satisfies at each iteration. In this paper, new methods will be explored for which the updated Hessians satisfy multiple relations of the Secant-type. A rational model is employed in developing the new methods. The model hosts a free parameter which is exploited in enforcing symmetry on the updated Hessian approximation matrix thus obtained. The numerical performance of such techniques is then investigated and compared to other methods. Our results are encouraging and the improvements incurred supercede those obtained from other existing methods at minimal extra storage and computational overhead.
机译:作者在[2]中推导了他们所谓的准牛顿多步法。这些方法已经证明了比标准的基于Secant的单步BFGS具有实质性的数值改进。此类方法使用Secant方程的变体,每次迭代时更新的Hessian(或其反函数)都满足。在本文中,将探索新的方法,使更新的Hessians满足Secant类型的多个关系。在开发新方法时采用了理性模型。该模型包含一个自由参数,该自由参数可用于对由此获得的更新的Hessian近似矩阵实施对称性。然后研究这种技术的数值性能,并将其与其他方法进行比较。我们的结果令人鼓舞,并且所进行的改进以最小的额外存储空间和计算开销取代了从其他现有方法获得的改进。

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