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New technique for solving univariate global optimization

Djamel Aaid;  Amel Noui;  Mohand Ouanes — 2017

Archivum Mathematicum

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...

Convex quadratic underestimation and Branch and Bound for univariate global optimization with one nonconvex constraint

Hoai An Le Thi;  Mohand Ouanes — 2006

RAIRO - Operations Research

The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with both twice differentiable function and constraint, we can propose an efficient algorithm based on Branch and Bound techniques. The method is first displayed in the simple case with an interval constraint. The extension is displayed afterwards to the general case with an additional nonconvex twice differentiable constraint. A quadratic bounding function which is better than the well known...

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