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SUMMARY:Lipschitz Global Optimization - Professor Yaroslav D Sergeyev\, Un
 iversita della Calabria
DTSTART:20180216T110000Z
DTEND:20180216T120000Z
UID:TALK95626@talks.cam.ac.uk
CONTACT:Pat Wilson
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 box
 \, multiextremal\, and non-differentiable. It is also assumed that evaluat
 ion of the objective function at a point is a time-consuming operation. Ma
 ny algorithms for solving this problem have been discussed in the literatu
 re. They can be distinguished\, for example\, by the way of obtaining info
 rmation about the Lipschitz constant and by the strategy of exploration of
  the search domain. Different exploration techniques based on various adap
 tive partition strategies are analyzed.\nThe main attention is dedicated t
 o two types of algorithms. The first of them is based on using space-filli
 ng curves in global optimization. A family of derivative-free numerical al
 gorithms applying space-filling curves to reduce the dimensionality of the
  global optimization problem is discussed. A number of unconventional idea
 s\, such as adaptive strategies for estimating Lipschitz constant\, balanc
 ing global and local information to accelerate the search\, etc. are prese
 nted.\nDiagonal global optimization algorithms is the second type of metho
 ds under consideration. They have a number of attractive theoretical prope
 rties and have proved to be efficient in solving applied problems. In thes
 e algorithms\, the search hyperinterval is adaptively partitioned into sma
 ller hyperintervals and the objective function is evaluated only at two ve
 rtices corresponding to the main diagonal of the generated hyperintervals.
  It is demonstrated that the traditional diagonal partition strategies do 
 not fulfil the requirements of computational efficiency because of executi
 ng many redundant evaluations of the objective function. A new adaptive di
 agonal partition strategy that allows one to avoid such computational redu
 ndancy is described. Some powerful multidimensional global optimization al
 gorithms based on the new strategy are introduced. Extensive numerical exp
 eriments are performed on the GKLS-generator that is used nowadays in more
  than 40 countries in the world to test numerical methods. Results of the 
 tests demonstrate that proposed methods outperform their competitors in te
 rms of both number of trials of the objective function and qualitative ana
 lysis of the search domain\, which is characterized by the number of gener
 ated hyperintervals. \nSelected references \n1.	Ya.D. Sergeyev\, R.G. Stro
 ngin\, and D. Lera\, Introduction to Global Optimization Exploiting Space-
 Filling Curves\, Springer\, New York\, 2013. \n2.	R.G. Strongin and Ya.D. 
 Sergeyev\, Global Optimization with Non-Convex Constraints: Sequential and
  Parallel Algorithms\, Springer\, New York\, 3rd ed.\, 2014.\n3.	Sergeyev 
 Ya.D.\, Kvasov D.E. Deterministic global optimization: An introduction to 
 the diagonal approach\, Springer\, New York\, 2017.\n
LOCATION:CBL Seminar Room
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