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. ***
