Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

0488869 - ÚI 2020 RIV NL eng J - Článek v odborném periodiku
Vlček, Jan - Lukšan, Ladislav
Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization.
Numerical Algorithms. Roč. 80, č. 3 (2019), s. 957-987. ISSN 1017-1398. E-ISSN 1572-9265
Grant CEP: GA ČR GA13-06684S
Institucionální podpora: RVO:67985807
Klíčová slova: Unconstrained minimization * Block variable metric methods * Limited-memory methods * BFGS update * Global convergence * Numerical results
Obor OECD: Applied mathematics
Impakt faktor: 2.064, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1007/s11075-018-0513-3

A block version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact that this formula satisfies the quasi-Newton conditions with all used difference vectors and that the improvement of convergence is the best one in some sense for quadratic objective functions, for general functions, it does not guarantee that the corresponding direction vectors are descent directions. To overcome this difficulty, but at the same time utilize the advantageous properties of the block BFGS update, a block version of the limited-memory variable metric BNS method for large-scale unconstrained optimization is proposed. The global convergence of the algorithm is established for convex sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.
Trvalý link: http://hdl.handle.net/11104/0283390