Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions

0369695 - ÚI 2012 CZ eng V - Výzkumná zpráva
Vlček, Jan - Lukšan, Ladislav
Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions.
Prague: ICS AS CR, 2011. 14 s. Technical Report, V-1127.
Grant CEP: GA ČR GA201/09/1957
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: unconstrained minimization * variable metric methods * limited-memory methods * the BFGS update * conjugate directions * preliminary numerical results
Kód oboru RIV: BA - Obecná matematika

Several modifications of the limited-memory variable metric BNS method for large scale un- constrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used difference 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 diffrence 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.
Trvalý link: http://hdl.handle.net/11104/0203700