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Dynamical systems and systems of equations

Tangencies and polynomial optimization

speaker: Tien Son Pham (University of Dalat)

abstract: Given a semi-algebraic function $f \colon S \rightarrow \mathbb{R}$ $(S \subset \mathbb{R}^n),$ we show that the following conditions may be characterized in terms of the tangency variety of $f$: (i) $f$ is bounded from below. (ii) $f$ attains its infimum. (iii) The sublevel sets $f \le t$ for $t \in \mathbb{R}$ are compact. (iv) $f$ is coercive.

timetable:
Tue 21 Jun, 17:40 - 18:40, Aula Dini
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