Optimization Letters

, Volume 2, Issue 3, pp 333–340 | Cite as

Convex underestimation for posynomial functions of positive variables

  • Han-Lin Li
  • Jung-Fa Tsai
  • Christodoulos A. Floudas
Original Paper

Abstract

The approximation of the convex envelope of nonconvex functions is an essential part in deterministic global optimization techniques (Floudas in Deterministic Global Optimization: Theory, Methods and Application, 2000). Current convex underestimation algorithms for multilinear terms, based on arithmetic intervals or recursive arithmetic intervals (Hamed in Calculation of bounds on variables and underestimating convex functions for nonconvex functions, 1991; Maranas and Floudas in J Global Optim 7:143–182, (1995); Ryoo and Sahinidis in J Global Optim 19:403–424, (2001)), introduce a large number of linear cuts. Meyer and Floudas (Trilinear monomials with positive or negative domains: Facets of convex and concave envelopes, pp. 327–352, (2003); J Global Optim 29:125–155, (2004)), introduced the complete set of explicit facets for the convex and concave envelopes of trilinear monomials with general bounds. This study proposes a novel method to underestimate posynomial functions of strictly positive variables.

Keywords

Convex envelopes Convex underestimators Posynomials 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Han-Lin Li
    • 1
  • Jung-Fa Tsai
    • 2
  • Christodoulos A. Floudas
    • 3
  1. 1.Institute of Information ManagementNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Department of Business ManagementNational Taipei University of TechnologyTaipeiTaiwan
  3. 3.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

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