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Solving generic nonarchimedean semidefinite programs using stochastic game algorithms

Xavier Allamigeon 1, 2 Stephane Gaubert 1, 2 Mateusz Skomra 1, 2 
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances.
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Contributor : Stephane Gaubert Connect in order to contact the contributor
Submitted on : Wednesday, January 3, 2018 - 12:02:23 AM
Last modification on : Friday, July 8, 2022 - 10:07:57 AM

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Xavier Allamigeon, Stephane Gaubert, Mateusz Skomra. Solving generic nonarchimedean semidefinite programs using stochastic game algorithms. Journal of Symbolic Computation, 2018, 85, pp.25-54. ⟨10.1016/j.jsc.2017.07.002⟩. ⟨hal-01674494⟩



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