eng
Vlček, Jan
Lukšan, Ladislav
Some modiﬁcations of the limited-memory variable metric optimization methods
unconstrained minimization
variable metric methods
limited-memory methods
variationally derived methods
arithmetic operations reduction
global convergence
https://hdl.handle.net/11104/0338248
http://www.nusl.cz/ntk/nusl-519915
http://invenio.nusl.cz/record/519915/files/0566981-vz1290-1.pdf
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.
2023