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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1007/bf00859469

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1573-2878

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A Generalization of the Classical Emphasis Type="

Authors: A Skjäl T Westerlund R Misener C A Floudas
Publish Date: 2012/03/30
Volume: 154, Issue: 2, Pages: 462-490
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Abstract

The classical αBB method determines univariate quadratic perturbations that convexify twice continuously differentiable functions This paper generalizes αBB to additionally consider nondiagonal elements in the perturbation Hessian matrix These correspond to bilinear terms in the underestimators where previously all nonlinear terms were separable quadratic terms An interval extension of Gerschgorin’s circle theorem guarantees convexity of the underestimator It is shown that underestimation parameters which are optimal in the sense that the maximal underestimation error is minimized can be obtained by solving a linear optimization modelTheoretical results are presented regarding the instantiation of the nondiagonal underestimator that minimizes the maximum error Two special cases are analyzed to convey an intuitive understanding of that optimallyselected convexifier Illustrative examples that convey the practical advantage of these new αBB underestimators are presentedAS gratefully acknowledges financial support from the Center of Excellence in Optimization and Systems Engineering at Åbo Akademi University CAF and RM are thankful for support from the National Science Foundation CBET – 0827907 This material is based upon work supported by the National Science Foundation Graduate Research Fellowship to RM under Grant No DGE0646086

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