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CATEGORIES:Engineering Design Centre Seminars
SUMMARY:Lipschitz Global Optimization - Prof Yaroslav Serg
eyev\, President of International Society of Globa
l Optimization
DTSTART;TZID=Europe/London:20181114T110000
DTEND;TZID=Europe/London:20181114T120000
UID:TALK112729AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112729
DESCRIPTION:Global optimization is a thriving branch of applie
d mathematics and an extensive literature is dedic
ated to it. In this lecture\, the global optimizat
ion problem of a multidimensional function satisfy
ing the Lipschitz condition over a hyperinterval w
ith an unknown Lipschitz constant is considered. I
t is supposed that the objective function can be `
`black box"\, multiextremal\, and non-differentiab
le. It is also assumed that evaluation of the obje
ctive function at a point is a time-consuming oper
ation. Many algorithms for solving this problem ha
ve been discussed in the literature. They can be d
istinguished\, for example\, by the way of obtaini
ng information about the Lipschitz constant and by
the strategy of exploration of the search domain.
Different exploration techniques based on various
adaptive partition strategies are analyzed.\nThe
main attention is dedicated to two types of algori
thms. The first of them is based on using space-fi
lling curves in global optimization. A family of d
erivative-free numerical algorithms applying space
-filling curves to reduce the dimensionality of th
e global optimization problem is discussed. A numb
er of unconventional ideas\, such as adaptive stra
tegies for estimating Lipschitz constant\, balanci
ng global and local information to accelerate the
search\, etc. are presented. Diagonal global optim
ization algorithms is the second type of methods u
nder consideration. They have a number of attracti
ve theoretical properties and have proved to be ef
ficient in solving applied problems. In these algo
rithms\, the search hyperinterval is adaptively pa
rtitioned into smaller hyperintervals and the obje
ctive function is evaluated only at two vertices c
orresponding to the main diagonal of the generated
hyperintervals. It is demonstrated that the tradi
tional diagonal partition strategies do not fulfil
the requirements of computational efficiency beca
use of executing many redundant evaluations of the
objective function. A new adaptive diagonal parti
tion strategy that allows one to avoid such comput
ational redundancy is described. Some powerful mul
tidimensional global optimization algorithms based
on the new strategy are introduced. Extensive num
erical experiments are performed on the GKLS-gener
ator that is used nowadays in more than 40 countri
es in the world to test numerical methods. Results
of the tests demonstrate that proposed methods ou
tperform their competitors in terms of both number
of trials of the objective function and qualitati
ve analysis of the search domain\, which is charac
terized by the number of generated hyperintervals.
\n
LOCATION:Sir Arthur Marshall Room\, Engineering Design Cent
re\, CUED
CONTACT:Mari Huhtala
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