Abstract
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.
Keywords
MathematicsSequence (biology)PolynomialLinear matrix inequalityCombinatoricsConvex optimizationRegular polygonSet (abstract data type)Discrete mathematicsApplied mathematicsPure mathematicsMathematical optimizationMathematical analysis
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Publication Info
- Year
- 2001
- Type
- article
- Volume
- 11
- Issue
- 3
- Pages
- 796-817
- Citations
- 2531
- Access
- Closed
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Cite This
Jean B. Lasserre
(2001).
Global Optimization with Polynomials and the Problem of Moments.
SIAM Journal on Optimization
, 11
(3)
, 796-817.
https://doi.org/10.1137/s1052623400366802
Identifiers
- DOI
- 10.1137/s1052623400366802