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SUMMARY:Lipschitz Global Optimization - Prof Yaroslav Sergeyev\, President
  of International Society of Global Optimization
DTSTART:20181114T110000Z
DTEND:20181114T120000Z
UID:TALK112729@talks.cam.ac.uk
CONTACT:Mari Huhtala
DESCRIPTION:Global optimization is a thriving branch of applied mathematic
 s and an extensive literature is dedicated to it. In this lecture\, the gl
 obal optimization problem of a multidimensional function satisfying the Li
 pschitz condition over a hyperinterval with an unknown Lipschitz constant 
 is considered. It is supposed that the objective function can be ``black b
 ox"\, multiextremal\, and non-differentiable. It is also assumed that eval
 uation of the objective function at a point is a time-consuming operation.
  Many algorithms for solving this problem have been discussed in the liter
 ature. They can be distinguished\, for example\, by the way of obtaining i
 nformation about the Lipschitz constant and by the strategy of exploration
  of the search domain. Different exploration techniques based on various a
 daptive partition strategies are analyzed.\nThe main attention is dedicate
 d to two types of algorithms. The first of them is based on using space-fi
 lling curves in global optimization. A family of derivative-free numerical
  algorithms applying space-filling curves to reduce the dimensionality of 
 the global optimization problem is discussed. A number of unconventional i
 deas\, such as adaptive strategies for estimating Lipschitz constant\, bal
 ancing global and local information to accelerate the search\, etc. are pr
 esented. Diagonal global optimization algorithms is the second type of met
 hods under consideration. They have a number of attractive theoretical pro
 perties and have proved to be efficient in solving applied problems. In th
 ese algorithms\, the search hyperinterval is adaptively partitioned into s
 maller hyperintervals and the objective function is evaluated only at two 
 vertices corresponding to the main diagonal of the generated hyperinterval
 s. It is demonstrated that the traditional diagonal partition strategies d
 o not fulfil the requirements of computational efficiency because of execu
 ting many redundant evaluations of the objective function. A new adaptive 
 diagonal partition strategy that allows one to avoid such computational re
 dundancy is described. Some powerful multidimensional global optimization 
 algorithms based on the new strategy are introduced. Extensive numerical e
 xperiments are performed on the GKLS-generator that is used nowadays in mo
 re than 40 countries in the world to test numerical methods. Results of th
 e tests demonstrate that proposed methods outperform their competitors in 
 terms of both number of trials of the objective function and qualitative a
 nalysis of the search domain\, which is characterized by the number of gen
 erated hyperintervals.\n
LOCATION:Sir Arthur Marshall Room\, Engineering Design Centre\, CUED
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