A Theoretical and Experimental Study of the Symmetric Rank One Update
Abstract
In this paper, we first discuss computational experience using the SR1 update in conventional line search and trust region algorithms for unconstrained optimization. Our experiments show that the SR1 is very competitive with the widely used BFGS method. They also indicate two interesting features: the final Hessian approximations produced by the SR1 method are not generally appreciably better than those produced by the BFGS, and the sequences of steps produced by the SR1 do not usually seem to have the uniform linear independence property that is assumed in some recent convergence analysis. We present a new analysis that shows that the SR1 method with a line search in n+1 step q-superlinearly convergent without assumption of linearly independent iterates. This analysis assumes that the Hessian approximations are positive definite and bounded asymptotically, which from our computational experience are reasonable assumptions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 31, 1990
- Accession Number
- ADA233965
Entities
People
- H. Khalfan
- R. B. Schnabel
- R. H. Byrd
Organizations
- University of Colorado Boulder