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Characterization and Computation of Real-Radical Ideals using Semidefinite Programming Techniques


Ph. Rostalski

2007 Spring Seminar of the "3ème cycle romand de Recherche Opérationnelle", Hôtel de l'Europe, Zinal, VS, Switzerland.

In this talk I will discuss a method (joined work with M. Laurent and J.-B. Lasserre) for computing all real points on a zero-dimensional semi-algebraic set described by polynomial equalities and inequalities as well as some "nice" polynomial generators for the corresponding vanishing ideal, namely border resp. Gröbner basis for the real radical ideal. In contrast to exact computational algebraic methods, the method we propose uses numerical linear algebra and semidefinite optimization techniques to compute approximate solutions and generator polynomials. The method is real-algebraic in nature and prevents the computation of any complex solution. The proposed methods fits well in a relatively new branch of mathematics called "Numerical Polynomial Algebra".


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