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

9403892 Ariyawansa该项目将开发和计算测试Davidon的共线缩放算法的变体，扩展了拟牛顿方法。这些算法将基于局部近似，以适当的迭代对目标函数值和梯度进行插值。它们将被设计成在圆锥函数上有有限终止，并且在共线标度下不变。这种算法的发展将开始与最近新的推导Davidon的共线缩放算法的主要研究者。计算实验将使用标准测试问题以及来自内点方法中使用的合适的势函数的测试实例。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产生实际的性能改进。如果计算实验表明，算法与Davidon的新的scaling和approximationcan提高性能优化潜在的功能，那么它将表明一个迄今为止尚未探索的方式发展更好的内点算法。由于内点方法具有广泛的适用性，这项工作可以揭示的研究机会，将在优化算法的重大进展。***

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. ***