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Mathematical Programming

, Volume 103, Issue 2, pp 207–224 | Cite as

Convex envelopes for edge-concave functions

  • Clifford A. Meyer
  • Christodoulos A. Floudas
Article

Abstract.

Deterministic global optimization algorithms frequently rely on the convex underestimation of nonconvex functions. In this paper we describe the structure of the polyhedral convex envelopes of edge-concave functions over polyhedral domains using geometric arguments. An algorithm for computing the facets of the convex envelope over hyperrectangles in ℝ3 is described. Sufficient conditions are described under which the convex envelope of a sum of edge-concave functions may be shown to be equivalent to the sum of the convex envelopes of these functions.

Keywords

Optimization Algorithm Global Optimization Mathematical Method Global Optimization Algorithm Polyhedral Convex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

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