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23rd European Symposium on Computer Aided Process Engineering by Ilkka Turunen, Andrzej Kraslawski

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comparison of two convex underestimation methods for quadratic functions

Anders Skjäl and Tapio Westerlund,    Center of Excellence in Optimization and Systems Engineering, Åbo Akademi University, Biskopsgatan 8, 20500 Åbo, Finland, anders.skjal@abo.fitapio.westerlund@abo.fi

Abstract

In this paper we compare two recently described methods for convex underestimation. The first method is a variant of the nondiagonal αBB methods studied by the authors. The second method depends on algebraic characterizations of positive polynomials. Positive polynomials on a compact semi-algebraic set can be decomposed as polynomial terms containing squares and the defining polynomials of the set. This characterization can be used for describing both the underestimation ...

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