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Randomized simplicial Hessian update
ID
Bürmen, Arpad
(
Avtor
),
ID
Tuma, Tadej
(
Avtor
),
ID
Olenšek, Jernej
(
Avtor
)
PDF - Predstavitvena datoteka,
prenos
(371,00 KB)
MD5: 62EB5A66D1E7BDF239A639BCED4DD874
URL - Izvorni URL, za dostop obiščite
https://www.mdpi.com/2227-7390/9/15/1775
Galerija slik
Izvleček
Recently, a derivative-free optimization algorithm was proposed that utilizes a minimum Frobenius norm (MFN) Hessian update for estimating the second derivative information, which in turn is used for accelerating the search. The proposed update formula relies only on computed function values and is a closed-form expression for a special case of a more general approach first published by Powell. This paper analyzes the convergence of the proposed update formula under the assumption that the points from $\mathbb{R}^n$ where the function value is known are random. The analysis assumes that the N + 2 points used by the update formula are obtained by adding N + 1 vectors to a central point. The vectors are obtained by transforming a prototype set of N + 1 vectors with a random orthogonal matrix from the Haar measure. The prototype set must positively span a N ≤ n dimensional subspace. Because the update is random by nature we can estimate a lower bound on the expected improvement of the approximate Hessian. This lower bound was derived for a special case of the proposed update by Leventhal and Lewis. We generalize their result and show that the amount of improvement greatly depends on N as well as the choice of the vectors in the prototype set. The obtained result is then used for analyzing the performance of the update based on various commonly used prototype sets. One of the results obtained by this analysis states that a regular n-simplex is a bad choice for a prototype set because it does not guarantee any improvement of the approximate Hessian.
Jezik:
Angleški jezik
Ključne besede:
derivative-free optimization
,
Hessian update
,
random matrices
,
uniform distribution
Vrsta gradiva:
Članek v reviji
Tipologija:
1.01 - Izvirni znanstveni članek
Organizacija:
FE - Fakulteta za elektrotehniko
Status publikacije:
Objavljeno
Različica publikacije:
Objavljena publikacija
Leto izida:
2021
Št. strani:
18 str.
Številčenje:
Vol. 9, iss. 15, art. 1775
PID:
20.500.12556/RUL-136022
UDK:
004
ISSN pri članku:
2227-7390
DOI:
10.3390/math9151775
COBISS.SI-ID:
87135235
Datum objave v RUL:
07.04.2022
Število ogledov:
608
Število prenosov:
104
Metapodatki:
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Objavi na:
Gradivo je del revije
Naslov:
Mathematics
Skrajšan naslov:
Mathematics
Založnik:
MDPI AG
ISSN:
2227-7390
COBISS.SI-ID:
523267865
Licence
Licenca:
CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
Povezava:
http://creativecommons.org/licenses/by/4.0/deed.sl
Opis:
To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
Začetek licenciranja:
01.08.2021
Sekundarni jezik
Jezik:
Slovenski jezik
Ključne besede:
optimizacija brez uporabe odvodov
,
posodabljanje Hessejeve matrike
,
naključne matrike
,
enakomerna porazdelitev
Projekti
Financer:
ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:
P2-0246
Naslov:
ICT4QoL - Informacijsko komunikacijske tehnologije za kakovostno življenje
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