Jun 22 – 26, 2015
Centre Paul-Langevin AUSSOIS
Europe/Paris timezone
In honor of Bernard Teissier's 70th birthday

Convexifying positive polynomials and a proximity algorithm

Not scheduled
Centre Paul-Langevin AUSSOIS

Centre Paul-Langevin AUSSOIS

Centre Paul-Langevin 24, rue du Coin 73500 Aussois


Mr Krzysztof Kurdyka (Université de Savoie)


We prove that if f is a positive C^2 function on a convex compact set X then it becomes strongly convex when multiplied by (1+|x|^2)^N with N large enough. For f polynomial we give an explicit estimate for N, which depends on the size of the coefficients of f and on the lower bound of f on X. As an application of our convexification method we propose an algorithm which for a given polynomial f on a convex compact semialgebraic set X produces a sequence (starting from an arbitrary point in X) which converges to a (lower) critical point of f on X. The convergence is based on the method of talweg which is a generalization of the Lojasiewicz gradient inequality. (Joint work with S. Spodzieja).

Presentation materials