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CATEGORIES:Machine Learning @ CUED
SUMMARY:Lipschitz Global Optimization - Professor Yaroslav
D Sergeyev\, Universita della Calabria
DTSTART;TZID=Europe/London:20180216T110000
DTEND;TZID=Europe/London:20180216T120000
UID:TALK95626AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/95626
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 b
lack box\, multiextremal\, and non-differentiable.
It is also assumed that evaluation of the objecti
ve function at a point is a time-consuming operati
on. Many algorithms for solving this problem have
been discussed in the literature. They can be dist
inguished\, for example\, by the way of obtaining
information about the Lipschitz constant and by th
e strategy of exploration of the search domain. Di
fferent exploration techniques based on various ad
aptive partition strategies are analyzed.\nThe mai
n attention is dedicated to two types of algorithm
s. The first of them is based on using space-filli
ng curves in global optimization. A family of deri
vative-free numerical algorithms applying space-fi
lling curves to reduce the dimensionality of the g
lobal optimization problem is discussed. A number
of unconventional ideas\, such as adaptive strateg
ies for estimating Lipschitz constant\, balancing
global and local information to accelerate the sea
rch\, etc. are presented.\nDiagonal global optimiz
ation algorithms is the second type of methods und
er consideration. They have a number of attractive
theoretical properties and have proved to be effi
cient in solving applied problems. In these algori
thms\, the search hyperinterval is adaptively part
itioned into smaller hyperintervals and the object
ive function is evaluated only at two vertices cor
responding to the main diagonal of the generated h
yperintervals. It is demonstrated that the traditi
onal diagonal partition strategies do not fulfil t
he requirements of computational efficiency becaus
e of executing many redundant evaluations of the o
bjective function. A new adaptive diagonal partiti
on strategy that allows one to avoid such computat
ional redundancy is described. Some powerful multi
dimensional global optimization algorithms based o
n the new strategy are introduced. Extensive numer
ical experiments are performed on the GKLS-generat
or that is used nowadays in more than 40 countries
in the world to test numerical methods. Results o
f the tests demonstrate that proposed methods outp
erform their competitors in terms of both number o
f trials of the objective function and qualitative
analysis of the search domain\, which is characte
rized by the number of generated hyperintervals. \
nSelected references \n1. Ya.D. Sergeyev\, R.G. St
rongin\, and D. Lera\, Introduction to Global Opti
mization Exploiting Space-Filling Curves\, Springe
r\, New York\, 2013. \n2. R.G. Strongin and Ya.D.
Sergeyev\, Global Optimization with Non-Convex Con
straints: Sequential and Parallel Algorithms\, Spr
inger\, New York\, 3rd ed.\, 2014.\n3. Sergeyev Ya
.D.\, Kvasov D.E. Deterministic global optimizatio
n: An introduction to the diagonal approach\, Spri
nger\, New York\, 2017.\n
LOCATION:CBL Seminar Room
CONTACT:Pat Wilson
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