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Convex relaxation for solving posynomial programs

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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 \({x_1^{\alpha _1 } x_2^{\alpha _2 }\ldots x_n^{\alpha _n } ,}\) 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 β j , for all α j > 0, such that \({y_j =x_j^{-\beta _j }}\) . By specifying β j carefully, we can find a tighter underestimation than the current methods.

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Authors and Affiliations

  1. Department of Information Management, College of Management Fu Jen Catholic University, No. 510, Jhongjheng Rd., Sinjhuang, Taipei , 242, Taiwan

    Hao-Chun Lu

  2. Institute of Information Management, National Chiao Tung University, Management Building 2, 1001 Ta-Hsueh Road, Hsinchu, 300, Taiwan

    Han-Lin Li

  3. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544, USA

    Chrysanthos E. Gounaris & Christodoulos A. Floudas

Authors
  1. Hao-Chun Lu
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  2. Han-Lin Li
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  3. Chrysanthos E. Gounaris
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  4. Christodoulos A. Floudas
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Correspondence to Hao-Chun Lu.

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Lu, HC., Li, HL., Gounaris, C.E. et al. Convex relaxation for solving posynomial programs. J Glob Optim 46, 147–154 (2010). https://doi.org/10.1007/s10898-009-9414-2

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