BFGS with Update Skipping and Varying Memory

Authors:
Tamara G. Kolda;Dianne P. O'Leary;Larry Nazareth
Affiliations:
-;-;-
Venue:
SIAM Journal on Optimization
Year:
1998

Citing 0
Cited 4

Extra-updates criterion for the limited memory BFGS Algorithm for large scale nonlinear optimization

Journal of Complexity
Updating the Self-Scaling Symmetric Rank One Algorithm with Limited Memory for Large-Scale Unconstrained Optimization

Computational Optimization and Applications
Efficient Solution of A, x(k) = b(k) Using A-1

Journal of Scientific Computing
L-Broyden methods: a generalization of the L-BFGS method to the limited-memory Broyden family

International Journal of Computer Mathematics

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Abstract

We give conditions under which limited-memory quasi-Newton methods with exact line searches will terminate in n steps when minimizing n-dimensional quadratic functions. We show that although all Broyden family methods terminate in n steps in their full-memory versions, only BFGS does so with limited-memory. Additionally, we show that full-memory Broyden family methods with exact line searches terminate in at most n + p steps when p matrix updates are skipped. We introduce new limited-memory BFGS variants and test them on nonquadratic minimization problems.