Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity

Authors:
Hayato Waki;Sunyoung Kim;Masakazu Kojima;Masakazu Muramatsu
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Optimization
Year:
2006

Citing 0
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Abstract

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.