A conjugate directions approach to improve the limited-memory BFGS method

0378976 - ÚI 2013 RIV US eng J - Článek v odborném periodiku
Vlček, Jan - Lukšan, Ladislav
A conjugate directions approach to improve the limited-memory BFGS method.
Applied Mathematics and Computation. Roč. 219, č. 3 (2012), s. 800-809. ISSN 0096-3003. E-ISSN 1873-5649
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 * numerical results
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.349, rok: 2012

Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors, utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. Global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly.
Trvalý link: http://hdl.handle.net/11104/0210274