Optimization Problems over Noncompact Semialgebraic Sets

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 will introduce how to compute the semidefinite representation or approximation of the convex hull of a noncompact semialgebraic set. Finally, we will show how to characterize the lifts of noncompact convex sets by the cone factorizations of properly defined slack operators.