Extended cutting angle method of global optimization

Beliakov, Gleb 2008, Extended cutting angle method of global optimization, Pacific journal of optimization, vol. 4, no. 1, pp. 153-176.

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Title Extended cutting angle method of global optimization
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Journal name Pacific journal of optimization
Volume number 4
Issue number 1
Start page 153
End page 176
Total pages 24
Publisher Yokohama Publishers
Place of publication Yokohama, Japan
Publication date 2008-01-01
ISSN 1348-9151
Keyword(s) global optimization
Lipschitz optimization
abstract convexity
cutting angle method
Sawtooth underestimate
Summary Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.
Language eng
Field of Research 010303 Optimisation
080205 Numerical Computation
010301 Numerical Analysis
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
HERDC collection year 2009
Copyright notice ©2008, Yokohama Publishers
Persistent URL http://hdl.handle.net/10536/DRO/DU:30017549

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