Minimizing the sum of many rational functions

  • We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of variables can be relatively large (10 to 100) provided some kind of sparsity is present. We describe a formulation of the rational optimization problem as a generalized moment problem and its hierarchy of convex semidefinite relaxations. Under some conditions we prove that the sequence of optimal values converges to the globally optimal value. We show how public-domain software can be used to model and solve such problems. Finally, we also compare with the epigraph approach and the BARON software.

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Metadaten
Author:Florian Bugarin, Didier Henrion, Jean Bernard Lasserre
DOI:https://doi.org/10.1007/s12532-015-0089-z
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2015
Tag:Software; Theoretical Computer Science
Volume:8
Issue:1
Page Number:29
First Page:83
Last Page:111
Mathematical Programming Computation :MPC 2016 - Issue 1
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