**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.

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

<< Go back