Convex relaxation for solving posynomial programs

Hao Chun Lu*, Han-Lin Li, Chrysanthos E. Gounaris, Christodoulos A. Floudas

*Corresponding author for this work

Research output: Contribution to journalArticle

15 Scopus citations

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 α1 x2 α2 ⋯ x n αn 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.

Original languageEnglish
Pages (from-to)147-154
Number of pages8
JournalJournal of Global Optimization
Volume46
Issue number1
DOIs
StatePublished - 1 Jan 2010

Keywords

  • Convex underestimation
  • Posynomial functions

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