Non-Quasi-Newton Updates for Unconstrained Optimization (Journal of Computational Mathematics, 1995)
In this report we present some new numerical methods for unconstrained optimization. These methods apply update formulae that do not satisfy the quasi-Newton equation. We derive these new formulae by considering different techniques of approximating the objective function. Theoretical analyses are given to show the advantages of using non-quasi-Newton updates. Under mild conditions we prove that our new update formulae preserve global convergence properties. Numerical results are also presented.