Semidefinite representations for finite varieties

@article{Laurent2007SemidefiniteRF,
  title={Semidefinite representations for finite varieties},
  author={Monique Laurent},
  journal={Mathematical Programming},
  year={2007},
  volume={109},
  pages={1-26}
}
  • M. Laurent
  • Published 2007
  • Mathematics, Computer Science
  • Mathematical Programming
We consider the problem of minimizing a polynomial over a set defined by polynomial equations and inequalities. When the polynomial equations have a finite set of complex solutions, we can reformulate this problem as a semidefinite programming problem. Our semidefinite representation involves combinatorial moment matrices, which are matrices indexed by a basis of the quotient vector space ℝ[x1, . . . ,xn]/I, where I is the ideal generated by the polynomial equations in the problem. Moreover, we… 
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