Davidon's Collinear Scaling Algorithms that Extend Quasi-Newton Methods for Optimization

该项目将开发和计算测试Davidon的共线缩放算法的变体，该算法扩展了准牛顿方法。这些算法将基于局部近似，在适当的迭代中插入目标函数值和梯度。它们将被设计成在二次函数上具有有限终止，并且在共线尺度下是不变的。这种算法的发展将开始于最近Davidon的共线缩放算法的新推导。计算实验将使用标准测试问题以及由内点法中使用的合适的势函数导出的测试实例。因此，拟议的项目将尝试以公正的方式评估利用Davidon的新缩放和近似所提供的全部潜力的算法是否会有实际的性能改进。如果计算实验表明Davidon的新缩放和近似算法可以提高优化势函数的性能，那么它将表明开发更好的内点算法的一种迄今尚未探索的方式。由于内点法具有广泛的适用性，因此这项工作可以揭示研究机会，从而在优化算法方面取得重大进展。＊＊＊

9403892 Ariyawansa This project will develop and computationally test variants of Davidon's collinear scaling algorithms that extend quasi-Newton methods. These algorithms would be based on local approximations that interpolate objective function values and gradients at suitable iterates. They would be designed to have finite termination on conic functions, and to be invariant under collinear scalings. The development of such algorithms would begin with the recent new derivation of Davidon's collinear scaling algorithms by the principal investigator. The computational experiments would use standard test problems as well as test instances derived from suitable potential functions used in interior point methods. The proposed project would thus attempt to assess in an unbiased manner whether algorithms that utilize the full potential offered by Davidon's new scalings and approximations would have practical performance improvements. If the computational experiments indicate that algorithms with Davidon's new scalings and approximationscan improve performance in optimizing potential functions, then it would indicate a hitherto unexplored way of developing better interior point algorithms. Since interior point methods have wide applicability, this work can reveal research opportunities that would make significant advancements in optimization algorithms. ***