Several modifications of the limited-memory variable metric BNS method for large scale unconstrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used di®erence vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all stored difference vectors and satisfaction of quasi-Newton conditions with these vectors is established. There are many possibilities how to realize this approach and although only two methods were implemented and tested, preliminary numerical results are promising.
Technical report No. V-1127, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07 Prague 8, Czech Republic, December 2011.