A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea

0444129 - ÚI 2016 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Vlček, Jan - Lukšan, Ladislav
A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea.
Programs and algorithms of numerical mathematics 17. Proceedings of seminar. Praha: Matematický ústav AV ČR, v.v.i, 2015 - (Chleboun, J.; Přikryl, P.; Segeth, K.; Šístek, J.; Vejchodský, T.), s. 237-243. ISBN 978-80-85823-64-6.
[Programs and Algorithms of Numerical Mathematics /17./. Dolní Maxov (CZ), 08.06.2014-13.06.2014]
Grant CEP: GA ČR GA13-06684S
Institucionální podpora: RVO:67985807
Klíčová slova: large scale unconstrained optimization * numerical experiments * limited-memory variable metric method * BNS method * quasi-Newton method * convergence
Kód oboru RIV: BA - Obecná matematika
http://dml.cz/handle/10338.dmlcz/702689

A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all stored corrected difference vectors are conjugate and the quasi-Newton conditions with these vectors are satisfied. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency.
Trvalý link: http://hdl.handle.net/11104/0246707