This article is cited in 16 papers

Cutting methods in $E^{n+1}$ for global optimization of a class of functions

V. P. Bulatov, O. V. Khamisov

Melentev Institute of Power Engineering Systems, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 130, Irkutsk, 664033, Russia

Abstract: A class of functions that attain their minima on a compact subset of the $n$-dimensional Euclidean space $E^n$ is introduced. This is a rather broad functional class, which is stable with respect to operations commonly occurring in optimization. The functions in this class are a convenient tool in the formal description of numerous applied problems. Moreover, reasonably efficient methods can be developed for finding global minima of such functions on a compact set. One such method is discussed in this paper.

Key words: global optimization, concave minorant, nonsingular matrix, cutting plane, cutting method.

UDC: 519.658

Received: 28.03.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:11, 1756–1767

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