Distinguished representations of strictly positive polynomials

By T. Jacobi, A. Prestel. 2001

125 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2373f9c803e7379befae792362f612477849e362

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Bounds on measures satisfying moment conditions (2002, background): “, Putinar [13], Jacobi [8], Jacobi and Prestel [9]).”
Positivity, sums of squares and the multi-dimensional moment problem II ⁄ (2005, methodology): “(yM ) is known to hold in a few cases, for example, if KS is compact and either n = 1 [ 7 ] or the polynomials g1;:::;gs are linear [7], [10] or s 2 [7].”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, background): “For a more advanced exposition on positivity and sums of squares and links to the moment problem, we refer in particular to the article by Scheiderer [125] and Schmüdgen [127] in this volume, to the survey article by Helton and Putinar [52], and to the monographs by Prestel and Delzell [114] and by”
SOS approximations of nonnegative polynomials via simple high degree perturbations (2005, background): “Prestel and Jacobi [ 6 ] then developed a valuation theoretic method for testing if this additional assumption, namely that the quadratic module is archimedean, is fulfilled.”
Positivity, sums of squares and the multi-dimensional moment problem (2002, methodology): “In [7], Jacobi and Prestel develop a powerful valuation-theoretic method for testing the validity of ( † M ) when K S is compact.”
A representation theorem for certain partially ordered commutative rings (2001, background): “[ H -W],p. 325) we see that every preordering is a generating preprime.”
Optimization of Polynomial Functions (2003, result): “According to results of Jacobi and Prestel [5] it is automatically satisfied in a variety of other cases as well.”
Distinguished representations of non-negative polynomials (2005, background): “Introduction Assume that we are given polynomials g1, . . . , gr with real coefficients in n variables, and another such polynomial f which is non-negative on the subset K := {g1 ≥ 0, . . . , gr ≥ 0} of Rn.”
Polynomials nonnegative on a grid and discrete optimization (2001, methodology): “10) and {U(x) ≥ 0} is compact (see Putinar [10], Jacobi and Prestel [4, 5]).”
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs (2006, background): “Although the validity of the required constraint qualification for compact polytopes has been established in [17] with techniques from real algebraic geometry, we will give a new proof based on Lagrange duality, which allows to extract explicit degree bounds.”
Representations of Non-Negative Polynomials, Degree Bounds and Applications to Optimization (2009, background): “This result extends to quadratic modules in various ways [ 3 ].”