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Estimados Académicos y Alumnos, <br>
<br>
Se les invita para el próximo Miércoles 25 de Mayo a las 16:30 hrs.
al Seminario Optimización y Equilibrio, el cual tendrá lugar en la
Sala de Seminarios John Von Neumann CMM. <br>
<br>
<b><i>SEMINARIO <br>
<br>
OPTIMIZACIÓN Y EQUILIBRIO<br>
<br>
EXPOSITOR <br>
Krzysztof Kurdyka
<br>
UNIVERSITE DE SAVOIE, France</i>
<i><br>
<br>
Title <br>
<br>
"Convexifying positive polynomials and a proximity algorithm"<br>
<br>
<br>
Abstract:</i></b><br>
<br>
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).
<br>
<br>
Miércoles 25 de Mayo a las 16:30 hrs, Sala de Seminarios John Von
Neumann CMM, séptimo piso, torre norte.<br>
<br>
Esperando contar con su asistencia les saluda, <br>
<br>
Ma. Inés Rivera <br>
<br>
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