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.
(Also cross-referenced as UMIACS-TR-96-49
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