Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods

Vlček, Jan, and Lukšan, Ladislav. "Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2019. 177-185. <http://eudml.org/doc/294914>.

@inProceedings{Vlček2019,
abstract = {To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy [16]. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method.},
author = {Vlček, Jan, Lukšan, Ladislav},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {unconstrained minimization; limited-memory variable metric methods; the repeated Byrd-Nocedal-Schnabel update; the Lyapunov matrix equation; the conjugate directions; global convergence; numerical results},
location = {Prague},
pages = {177-185},
publisher = {Institute of Mathematics CAS},
title = {Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods},
url = {http://eudml.org/doc/294914},
year = {2019},
}

TY - CLSWK
AU - Vlček, Jan
AU - Lukšan, Ladislav
TI - Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2019
CY - Prague
PB - Institute of Mathematics CAS
SP - 177
EP - 185
AB - To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy [16]. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method.
KW - unconstrained minimization; limited-memory variable metric methods; the repeated Byrd-Nocedal-Schnabel update; the Lyapunov matrix equation; the conjugate directions; global convergence; numerical results
UR - http://eudml.org/doc/294914
ER -