TY - RPRT
TI - Some modiﬁcations of the limited-memory variable metric optimization methods
AU - Vlček, Jan
AB - Several modiﬁcations of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modiﬁed to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new eﬃcient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
UR - http://www.nusl.cz/ntk/nusl-519915
UR - https://hdl.handle.net/11104/0338248
A2 - Lukšan, Ladislav
LA - eng
KW - variable metric methods
KW - unconstrained minimization
KW - variationally derived methods
KW - global convergence
KW - limited-memory methods
KW - arithmetic operations reduction
UR - http://invenio.nusl.cz/record/519915/files/0566981-vz1290-1.pdf
PY - 2023
PB - Ústav informatiky, Pod vodárenskou věží 2, 182 07 Praha 8, http://www.cs.cas.cz/
ER -