Global Optimization with Polynomials and the Problem of Moments

@article{Lasserre2001GlobalOW,
  title={Global Optimization with Polynomials and the Problem of Moments},
  author={Jean B. Lasserre},
  journal={SIAM J. Optim.},
  year={2001},
  volume={11},
  pages={796-817}
}
  • J. Lasserre
  • Published 1 March 2000
  • Mathematics
  • SIAM J. Optim.
We consider the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): {\mathbb{R}}^n\to {\mathbb{R}}$, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush--Kuhn--Tucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided. 
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