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Polynomials Nonnegative on a Grid and Discrete Optimization

Jean B. Lasserre
Transactions of the American Mathematical Society
Vol. 354, No. 2 (Feb., 2002), pp. 631-649
Stable URL: http://www.jstor.org/stable/2693763
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Polynomials Nonnegative on a Grid and Discrete Optimization
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Abstract

We characterize the real-valued polynomials on Rn that are non-negative (not necessarily strictly positive) on a grid K of points of Rn, in terms of a weighted sum of squares whose degree is bounded and known in advance. We also show that the mimimization of an arbitrary polynomial on K (a discrete optimization problem) reduces to a convex continuous optimization problem of fixed size. The case of concave polynomials is also investigated. The proof is based on a recent result of Curto and Fialkow on the K-moment problem.

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