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Compact Relaxations for Polynomial Programming Problems

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7276)

Abstract

Reduced RLT constraints are a special class of Reformulation-Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach.

Keywords

  • polynomial
  • nonconvex
  • MINLP
  • sBB
  • reformulation
  • convex relaxation
  • RLT

We are grateful to Dr. Tatjana Davidović and Christoph Dürr for useful discussions. Financial support by grants: Digiteo Chair 2009-14D “RMNCCO”, Digiteo Emergence 2009-55D “ARM” is gratefully acknowledged.

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Cafieri, S., Hansen, P., Létocart, L., Liberti, L., Messine, F. (2012). Compact Relaxations for Polynomial Programming Problems. In: Klasing, R. (eds) Experimental Algorithms. SEA 2012. Lecture Notes in Computer Science, vol 7276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30850-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-30850-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30849-9

  • Online ISBN: 978-3-642-30850-5

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