Nonnegative Morse polynomial functions and polynomial optimization

Nonnegative Morse polynomial functions and polynomial optimization In this paper we study the representation of Morse polynomial functions which are nonnegative on a compact basic closed semi-algebraic set in $$\mathbb R^{n}$$ R n , and having only finitely many zeros in this set. Following Bivià-Ausina (Math Z 257:745–767, 2007), we introduce two classes of non-degenerate polynomials for which the algebraic sets defined by them are compact. As a consequence, we study the representation of nonnegative Morse polynomials on these kinds of non-degenerate algebraic sets. Moreover, we apply these results to study the polynomial optimization problem for Morse polynomial functions. Positivity Springer Journals

Nonnegative Morse polynomial functions and polynomial optimization

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Springer International Publishing
Copyright © 2015 by Springer Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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