New Parameterizations for Multi-Step Unconstrained Optimization

  • Moghrabi, I.A. (Department of Computer Science Lebanese American University) ;
  • Kassar, A.N (Faculty of Science, Beirut Arab University)
  • Published : 1999.06.30


We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi [1, 2], who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms.