TY - JOUR
T1 - Convex relaxation for solving posynomial programs
AU - Lu, Hao Chun
AU - Li, Han-Lin
AU - Gounaris, Chrysanthos E.
AU - Floudas, Christodoulos A.
N1 - Funding Information:
Acknowledgments The authors thank the area editor, the anonymous associate editor, and anonymous referees for providing insightful comments that significantly improved this paper. This research has been supported by Taiwan NSC 97-2218-E-030-005-.
PY - 2010/1
Y1 - 2010/1
N2 - 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 1α1 x2α2 ⋯ x nαn 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 β j, for all α j > 0, such that yj =xj-βj. By specifying β j carefully, we can find a tighter underestimation than the current methods.
AB - 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 1α1 x2α2 ⋯ x nαn 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 β j, for all α j > 0, such that yj =xj-βj. By specifying β j carefully, we can find a tighter underestimation than the current methods.
KW - Convex underestimation
KW - Posynomial functions
UR - http://www.scopus.com/inward/record.url?scp=72449165495&partnerID=8YFLogxK
U2 - 10.1007/s10898-009-9414-2
DO - 10.1007/s10898-009-9414-2
M3 - Article
AN - SCOPUS:72449165495
SN - 0925-5001
VL - 46
SP - 147
EP - 154
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 1
ER -