Geodesic
Multiple update multi-step methods for unconstrained optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 47-53

Voir la notice de l'article provenant de la source Math-Net.Ru

The quasi-Newton multi-step methods were developed in [2] and have revealed substantial numerical improvements over the standard single step Secant-based BFGS. Such methods use a variant of the Secant equation that the updated Hessian (or its inverse) satisfies at each iteration. In this paper, we explore algorithms whose updated Hessians satisfy multiple relations of the Secant-type in order that the numerical potentials of such techniques be investigated. We employ a rational model in developing the new methods. The model hosts a free parameter which is exploited in enforcing symmetry on the multi-updated matrix. Our results are encouraging, and the improvements incurred supercede those obtained from other existing methods at minimal extra storage and computational overhead. 
@article{SJVM_2006_9_1_a4,
     author = {I. Moghrabi},
     title = {Multiple update multi-step methods for unconstrained optimization},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {47--53},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a4/}
}
TY  - JOUR
AU  - I. Moghrabi
TI  - Multiple update multi-step methods for unconstrained optimization
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2006
SP  - 47
EP  - 53
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a4/
LA  - en
ID  - SJVM_2006_9_1_a4
ER  - 
%0 Journal Article
%A I. Moghrabi
%T Multiple update multi-step methods for unconstrained optimization
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2006
%P 47-53
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a4/
%G en
%F SJVM_2006_9_1_a4
I. Moghrabi. Multiple update multi-step methods for unconstrained optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 47-53. http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a4/