BFGS WITH UPDATE SKIPPING AND VARYING MEMORY

We give conditions under which limited-memory quasi-Newton methods wit h exact line searches will terminate in n steps when minimizing n-dime nsional 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 Br oyden family methods with exact line searches terminate in at most n p steps when p matrix updates are skipped. We introduce new limited-m emory BFGS variants and test them on nonquadratic minimization problem s.