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Abstract: We consider here the problem of minimizing a polynomial function on R . The problem is known to be hard even for degree 4. Therefore approximation algorithms are of interest. Lasserre [11] and Parrilo [16] have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We propose here a method for computing a converging sequence of upper bounds using semidefinite programming based on perturbing the original... (Update)
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BibTeX entry: (Update)
D. Jibetean and M. Laurent. Converging semidefinite bounds for global unconstrained polynomial optimization. Preprint, 2004. http://citeseer.ist.psu.edu/jibetean04converging.html More
@misc{ jibetean04converging,
author = "D. Jibetean and M. Laurent",
title = "Converging semidefinite bounds for global unconstrained polynomial optimization",
text = "D. Jibetean and M. Laurent. Converging semidefinite bounds for global unconstrained
polynomial optimization. Preprint, 2004.",
year = "2004",
url = "citeseer.ist.psu.edu/jibetean04converging.html" }
Citations (may not include all citations):51 Global optimization with polynomials and the problem of mome.. - Lasserre - 2001
48 varieties and algorithms (context) - Cox, Little et al. - 1997
40 Structured Semidefinite Programs and Semialgebraic Geometry .. - Parrilo - 2000
39 Transactions of the American Mathematical Society (context) - Curto, Fialkow et al. - 2000
37 Some NP-complete problems in quadratic and nonlinear program.. (context) - Murty, Kabadi - 1987
30 Positive polynomials on compact semialgebraic sets (context) - Putinar - 1993
27 Semidefinite programming relaxations for semialgebraic probl.. - Parrilo - 2003
20 Class of global minimum bounds of polynomial functions (context) - Shor - 1987
16 GloptiPoly: Global optimization over polynomials with Matlab.. - Henrion, Lasserre - 2003
5 Solution of the truncated complex moment problem for flat da.. (context) - Curto, Fialkow - 1996
4 Global minimization of a multivariate polynomial using matri.. (context) - Hanzon, Jibetean - 2003
4 Computing global minima to polynomial optimization problems .. (context) - Hagglof, Lindberg et al. - 1995
3 Linear Algebra and its Applications (context) - Kaplan, for et al. - 2000
3 Detecting global optimality and extracting solutions in Glop.. (context) - Henrion, Lasserre - 2003
2 Semidefinite representations for finite varieties - Laurent - 2002
2 Algebraic optimization with applications to system theory (context) - Jibetean - 2003
2 Symbolic recipes for real solutions (context) - Gonzalez-Vega, Rouillier et al. - 1999
1 Revisiting two theorems of Curto and Fialkow about moment ma.. (context) - Laurent - 2004
1 Uniform denominators in Hilbert's 17th problem (context) - Reznick - 1995
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