The Effect of Hessian Evaluations in the Global Optimization αBB Method

Milan Hladík ()
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Milan Hladík: Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics

A chapter in Modeling, Simulation and Optimization of Complex Processes HPSC 2015, 2017, pp 67-79 from Springer

Abstract: Abstract We consider convex underestimators that are used in the global optimization αBB method and its variants. The method is based on augmenting the original nonconvex function by a relaxation term that is derived from an interval enclosure of the Hessian matrix. In this paper, we discuss the advantages of symbolic computation of the Hessian matrix. Symbolic computation often allows simplifications of the resulting expressions, which in turn means less conservative underestimators. We show by examples that even a small manipulation with the symbolic expressions, which can be processed automatically by computers, can have a large effect on the quality of underestimators. The purpose of this paper is also to turn attention of researchers to the possibility of symbolic differentiation (and its combination with automatic differentiation) and investigation of the most convenient way for interval evaluation.

Keywords: Convex Underestimator; Automatic Differentiation; Interval Enclosure; Original Nonconvex Function; Interval Evaluation (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-67168-0_6

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DOI: 10.1007/978-3-319-67168-0_6

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