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pro vyhledávání: '"Baldi, Lorenzo"'
We study the problem of representing multivariate polynomials with rational coefficients, which are nonnegative and strictly positive on finite semialgebraic sets, using rational sums of squares. We focus on the case of finite semialgebraic sets S de
Externí odkaz:
http://arxiv.org/abs/2410.04845
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic study of the facial structure of the cone of nonnegative polynomials $\pos
Externí odkaz:
http://arxiv.org/abs/2407.06017
Autor:
Baldi, Lorenzo, Slot, Lucas
The Positivstellens\"atze of Putinar and Schm\"udgen show that any polynomial $f$ positive on a compact semialgebraic set can be represented using sums of squares. Recently, there has been large interest in proving effective versions of these results
Externí odkaz:
http://arxiv.org/abs/2302.12558
The representation of positive polynomials on a semi-algebraic set in terms of sums of squares is a central question in real algebraic geometry, which the Positivstellensatz answers. In this paper, we study the effective Putinar's Positivestellensatz
Externí odkaz:
http://arxiv.org/abs/2212.09551
Publikováno v:
In Journal of Algebra 15 January 2025 662:741-767
Autor:
Baldi, Lorenzo, Mourrain, Bernard
We analyse the representation of positive polynomials in terms of Sums of Squares. We provide a quantitative version of Putinar's Positivstellensatz over a compact basic semialgebraic set S, with a new polynomial bound on the degree of the positivity
Externí odkaz:
http://arxiv.org/abs/2111.11258
Autor:
Baldi, Lorenzo, Mourrain, Bernard
We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generic linear functional vanishing on the generators of is computed solving
Externí odkaz:
http://arxiv.org/abs/2102.09367
Autor:
Baldi, Lorenzo, Mourrain, Bernard
We investigate the problem of representing moment sequences by measures in the context ofPolynomial Optimization Problems. This consists in finding the infimum of a real polynomial ona real semialgebraic set defined by polynomial inequalities. We ana
Externí odkaz:
http://arxiv.org/abs/2012.14652
Autor:
Baldi, Lorenzo1 (AUTHOR) lorenzo.baldi@inria.fr, Mourrain, Bernard1 (AUTHOR)
Publikováno v:
Mathematical Programming. Jun2023, Vol. 200 Issue 1, p71-103. 33p.
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