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Article Dans Une Revue Mathematical Programming Computation Année : 2018

Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity

Résumé

We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the running intersection property this Sparse-BSOS hierarchy of semidefinite programs (with semidefinite constraints of fixed size) converges to the global optimum of the original problem. Moreover, for the class of SOS-convex problems, finite convergence takes place at the first step of the hierarchy, just as in the dense version.
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Dates et versions

hal-01341931 , version 1 (05-07-2016)
hal-01341931 , version 2 (03-03-2017)
hal-01341931 , version 3 (26-05-2017)

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Tillmann Weisser, Jean-Bernard Lasserre, Kim-Chuan Toh. Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity. Mathematical Programming Computation, 2018, 10, pp.1--32. ⟨hal-01341931v3⟩
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