Optimizing a linear function over a noncompact real algebraic variety

In this talk, we will introduce some recent progress in dealing with optimization problems over noncompact semialgebraic sets. We will start with the problem of optimizing a parametric linear function over a noncompact real algebraic variety. Then we ...

The "bottom" of a partially ordered set (poset) Q is the set Q of its lower bounds (hence, Q is empty or a singleton). The poset Q is said to be atomic if each element of Q Q dominates an atom, that is, a minimal element of Q Q . Thus, all finite posets ...

In this paper we study the variety M _nil of nilpotent elements of a reductive monoid M . In general this variety has a completely different structure than the variety G _uni of unipotent elements of the unit group G of M . When M has a ...