Some numerical experiments with variable-storage quasi-Newton algorithms

Some numerical experiments with variable-storage quasi-Newton algorithms

Updating Quasi - Newton Matrices With Limited Storage By Jorge Nocedal

We study how to use the BFGS quasi-Newton matrices to precondition minimization methods for problems where the storage is critical. We give an update formula which generates matrices using information from the last m iterations, where m is any number supplied by the user. The quasi-Newton matrix is updated at every iteration by dropping the oldest information and replacing it by the newest info...

Variable-storage quasi-Newton operators as inverse forecast/analysis error covariance matrices in variational data assimilation

Two approximations of the Hessian matrix as limited-memory operators are built from the limited-memoryBFGS inverse Hessian approximationprovided by the minimization code, in view of the speci cation of the inverse analysis/forecast error covariance matrix in variational data assimilation. Some numerical experiments and theoretical considerations lead to reject the limited-memory DFP Hessian app...

Numerical Experience with Limited-Memory Quasi-Newton and Truncated Newton Methods

Computational experience with several limited-memory quasi-Newton and truncated Newton methods for unconstrained nonlinear optimization is described. Comparative tests were conducted on a well-known test library [J. on several synthetic problems allowing control of the clustering of eigenvalues in the Hessian spectrum, and on some large-scale problems in oceanography and meteorology. The result...

Some Experiments with Real-time Decision Algorithms

Real-time Decision algorithms are a class of incremental resource-bounded [Horvitz, 89] or anytime [Dean, 93] algorithms for evaluating influence diagrams. We present a test domain for real-time decision algorithms, and the results of experiments with several Real-time Decision Algorithms in this domain. The results demonstrate high performance for two algorithms, a decision-evaluation variant ...