%0 Journal Article %J SIAM Journal on Optimization %D 1998 %T BFGS with Update Skipping and Varying Memory %A Kolda,Tamara G. %A O'Leary, Dianne P. %A Nazareth,Larry %K bfgs %K Broyden family %K limited-memory %K minimization %K quasi-Newton %K update skipping %X 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. %B SIAM Journal on Optimization %V 8 %P 1060 - 1083 %8 1998/// %G eng %U http://link.aip.org/link/?SJE/8/1060/1 %N 4 %R 10.1137/S1052623496306450