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Journal of Global Optimization

, Volume 25, Issue 2, pp 157–168 | Cite as

Convex Envelopes of Monomials of Odd Degree

  • Leo Liberti
  • Constantinos C. PantelidesEmail author
Article

Abstract

Convex envelopes of nonconvex functions are widely used to calculate lower bounds to solutions of nonlinear programming problems (NLP), particularly within the context of spatial Branch-and-Bound methods for global optimization. This paper proposes a nonlinear continuous and differentiable convex envelope for monomial terms of odd degree, x2k+1, where k ∈ N and the range of x includes zero. We prove that this envelope is the tightest possible. We also derive a linear relaxation from the proposed envelope, and compare both the nonlinear and linear formulations with relaxations obtained using other approaches.

Cubic Odd degree Monomial Convex relaxation Global optimization 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  1. 1.Centre for Process Systems EngineeringImperial College of Science, Technology and MedicineLondonUK

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