Title: Convex relaxation for solving posynomial programs
Authors: Lu, Hao-Chun
Li, Han-Lin
Gounaris, Chrysanthos E.
Floudas, Christodoulos A.
資訊管理與財務金融系 註:原資管所+財金所
Department of Information Management and Finance
Keywords: Convex underestimation;Posynomial functions
Issue Date: 1-Jan-2010
Abstract: Convex underestimation techniques for nonlinear functions are an essential part of global optimization. These techniques usually involve the addition of new variables and constraints. In the case of posynomial functions x(1)(alpha 1)x(2)(alpha 2) ... x(n)(alpha n), logarithmic transformations (Maranas and Floudas, Comput. Chem. Eng. 21: 351-370, 1997) are typically used. This study develops an effective method for finding a tight relaxation of a posynomial function by introducing variables y(j) and positive parameters beta(j), for all alpha(j) > 0, such that y(j) = x(j)(-beta j). By specifying beta(j) carefully, we can find a tighter underestimation than the current methods.
URI: http://dx.doi.org/10.1007/s10898-009-9414-2
ISSN: 0925-5001
DOI: 10.1007/s10898-009-9414-2
Volume: 46
Issue: 1
Begin Page: 147
End Page: 154
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