Abstract
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.
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