New technique for solving univariate global optimization

Djamel Aaid, Amel Noui, and Mohand Ouanes

D. Aaid, Département de Mathématiques, Université de Constantine, Algérie, Département du socle commun SNV, Université de Batna 2, Algerie, Laboratoire d’Informatique Théorique et Appliquée (LITA), Université de Lorraine, 57045 Metz cedex 1-France
A. Noui, Département de Mathématiques, Université de Constantine 1, Algérie, Département de Mathématiques, Université de Batna 2, Algérie
M. Ouanes, Département de Mathématiques, Université de Tizi-Ouzou, Algérie


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.

AMSclassification: primary 90C26; secondary 90C30.

Keywords: global optimization, Branch and Bound method, convex underestimation, piecewise quadratic, explicit solution.

DOI: 10.5817/AM2017-1-19