Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 17, Issue 1, Pages 218-242Publisher
SIAM PUBLICATIONS
DOI: 10.1137/050623802
Keywords
polynomial optimization problem; sparsity; global optimization; Lagrangian relaxation; Lagrangian dual; sums of squares optimization; semidefinite program relaxation
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Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of the supports for sums of squares ( SOS) polynomials that lead to efficient SOS and semidefinite program ( SDP) relaxations are obtained. Numerical results from various test problems are included to show the improved performance of the SOS and SDP relaxations.
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