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Global Optimization of Mixed-Integer Signomial Programming Problems

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Book cover Mixed Integer Nonlinear Programming

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 154))

Abstract

Described in this chapter, is a global optimization algorithm for mixedinteger nonlinear programming problems containing signomial functions. The method obtains a convex relaxation of the nonconvex problem through reformulations using single-variable transformations in combination with piecewise linear approximations of the inverse transformations. The solution of the relaxed problems converges to the global optimal solution as the piecewise linear approximations are improved iteratively. To illustrate how the algorithm can be used to solve problems to global optimality, a numerical example is also included.

AMS(MOS) subject classifications. 90C11, 90C26, 90C30.

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Author information

Authors and Affiliations

  1. Process Design and Systems Engineering, Åbo Akademi University, FIN-20500, Turku, Finland

    Andreas Lundell & Tapio Westerlund

Authors
  1. Andreas Lundell
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  2. Tapio Westerlund
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Corresponding author

Correspondence to Andreas Lundell .

Editor information

Editors and Affiliations

  1. , College of Engineering, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, 48109, Michigan, USA

    Jon Lee

  2. , Mathematics and Computer Science, Argonne National Laboratory, Argonne, 60439, Illinois, USA

    Sven Leyffer

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Lundell, A., Westerlund, T. (2012). Global Optimization of Mixed-Integer Signomial Programming Problems. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1927-3_12

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