Optimization of Unconstrained Functions with Sparse Hessian Matrices -- Quasi-Newton Methods.
Abstract
Newton-type methods and quasi-Newton methods have proven to be very successful in solving dense unconstrained optimization problems. Recently there has been considerable interest in extending these methods to solving large problems when the Hessian matrix has a known a priori sparsity pattern. This paper treats sparse quasi-Newton methods in a uniform fashion and shows the effect of loss of positive-definiteness in generating updates. These sparse quasi-Newton methods coupled with a modified Cholesky factorization to take into account the loss of positive-definiteness when solving the linear systems associated with these methods were tested on a large set of problems. The overall conclusions are that these methods perform poorly in general-the Hessian matrix becomes indefinite even close to the solution and superlinear convergence is not observed in practice. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1981
- Accession Number
- ADA106028
Entities
People
- Mukund N. Thapa
Organizations
- Stanford University