Showing papers by "John E. Dennis published in 1980"
01 Aug 1980
TL;DR: In this paper, a simple new set of techniques for deriving symmetric and positive definite secant updates was introduced, and applied to generate a new projected BFGS update, and indicate applications to the efficient implementation of secant algorithms via the Cholesky factorization.
Abstract: In this paper, we introduce a simple new set of techniques for deriving symmetric and positive definite secant updates. We use these techniques to present a simple new derivation of the BFGS update using neither matrix inverses nor weighting matrices. A related derivation is shown to generate a large class of symmetric rank-two update formulas, together with the condition for each to preserve positive definiteness. We apply our techniques to generate a new projected BFGS update, and indicate applications to the efficient implementation of secant algorithms via the Cholesky factorization.
34 citations