New technique for solving univariate global optimization

Djamel Aaid; Amel Noui; Mohand Ouanes

Archivum Mathematicum (2017)

  • Volume: 053, Issue: 1, page 19-33
  • ISSN: 0044-8753

Abstract

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In this paper, a new global optimization method is proposed for an optimization problem with twice differentiable objective function a single variable with box constraint. The method employs a difference of linear interpolant of the objective and a concave function, where the former is a continuous piecewise convex quadratic function underestimator. The main objectives of this research are to determine the value of the lower bound that does not need an iterative local optimizer. The proposed method is proven to have a finite convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering methods.

How to cite

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Aaid, Djamel, Noui, Amel, and Ouanes, Mohand. "New technique for solving univariate global optimization." Archivum Mathematicum 053.1 (2017): 19-33. <http://eudml.org/doc/287965>.

@article{Aaid2017,
abstract = {In this paper, a new global optimization method is proposed for an optimization problem with twice differentiable objective function a single variable with box constraint. The method employs a difference of linear interpolant of the objective and a concave function, where the former is a continuous piecewise convex quadratic function underestimator. The main objectives of this research are to determine the value of the lower bound that does not need an iterative local optimizer. The proposed method is proven to have a finite convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering methods.},
author = {Aaid, Djamel, Noui, Amel, Ouanes, Mohand},
journal = {Archivum Mathematicum},
keywords = {global optimization; Branch and Bound method; convex underestimation; piecewise quadratic; explicit solution},
language = {eng},
number = {1},
pages = {19-33},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {New technique for solving univariate global optimization},
url = {http://eudml.org/doc/287965},
volume = {053},
year = {2017},
}

TY - JOUR
AU - Aaid, Djamel
AU - Noui, Amel
AU - Ouanes, Mohand
TI - New technique for solving univariate global optimization
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 1
SP - 19
EP - 33
AB - In this paper, a new global optimization method is proposed for an optimization problem with twice differentiable objective function a single variable with box constraint. The method employs a difference of linear interpolant of the objective and a concave function, where the former is a continuous piecewise convex quadratic function underestimator. The main objectives of this research are to determine the value of the lower bound that does not need an iterative local optimizer. The proposed method is proven to have a finite convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering methods.
LA - eng
KW - global optimization; Branch and Bound method; convex underestimation; piecewise quadratic; explicit solution
UR - http://eudml.org/doc/287965
ER -

References

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