Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems

Dmitri E. Kvasov

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 857-871
  • ISSN: 0392-4041

Abstract

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This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, a global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice that explains a great interest of researchers to the stated problem. A new diagonal scheme which is aimed for developing fast global optimization algorithms is presented, and several such algorithms are introduced and examined. Theoretical and experimental studies performed confirm the benefit of the new approach over traditionally used diagonal global optimization methods.

How to cite

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Kvasov, Dmitri E.. "Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 857-871. <http://eudml.org/doc/290452>.

@article{Kvasov2008,
abstract = {This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, a global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice that explains a great interest of researchers to the stated problem. A new diagonal scheme which is aimed for developing fast global optimization algorithms is presented, and several such algorithms are introduced and examined. Theoretical and experimental studies performed confirm the benefit of the new approach over traditionally used diagonal global optimization methods.},
author = {Kvasov, Dmitri E.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {857-871},
publisher = {Unione Matematica Italiana},
title = {Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems},
url = {http://eudml.org/doc/290452},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Kvasov, Dmitri E.
TI - Diagonal Numerical Methods for Solving Lipschitz Global Optimization Problems
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 857
EP - 871
AB - This paper briefly describes some results of the author's PhD thesis, which has been specially mentioned by the Italian INdAM-SIMAI Committee for the Competition "The Best PhD Thesis in Applied Mathematics defended in 2004-2006". In this work, a global optimization problem is considered where the objective function is a multidimensional black-box function satisfying the Lipschitz condition over a hyperinterval and hard to evaluate. Such functions are frequently encountered in practice that explains a great interest of researchers to the stated problem. A new diagonal scheme which is aimed for developing fast global optimization algorithms is presented, and several such algorithms are introduced and examined. Theoretical and experimental studies performed confirm the benefit of the new approach over traditionally used diagonal global optimization methods.
LA - eng
UR - http://eudml.org/doc/290452
ER -

References

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