ACM Transactions on Mathematical Software (TOMS)
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones
Computational Optimization and Applications
Solving polynomial least squares problems via semidefinite programming relaxations
Journal of Global Optimization
International Journal of Automation and Computing
Convergent SDP-relaxations for polynomial optimization with sparsity
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity
Journal of Global Optimization
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Sequences of generalized Lagrangian duals and their sums of squares (SOS) of polynomials relaxations for a polynomial optimization problem (POP) are introduced. The sparsity of polynomials in the POP is used to reduce the sizes of the Lagrangian duals and their SOS relaxations. It is proved that the optimal values of the Lagrangian duals in the sequence converge to the optimal value of the POP using a method from the penalty function approach. The sequence of SOS relaxations is transformed into a sequence of semidefinite programing (SDP) relaxations of the POP, which correspond to duals of modification and generalization of SDP relaxations given by Lasserre for the POP.