实凸集上的线性化函子
Linearization functors on real convex sets
摘要：
我们证明了线性化某些族的多项式最优化问题，导致新的函子运算在真正的凸集。我们表明，在某些条件下，这些操作可以计算或近似的方式服从有效的计算。这些操作是凸类似物的霍姆函子，张量积，对称的权力，外部权力和一般舒尔函子向量空间，并导致新的建设，甚至多面体。
英文摘要：
We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to efficient computation. These operations are convex analogues of Hom functors, tensor products, symmetric powers, exterior powers and general Schur functors on vector spaces and lead to novel constructions even for polyhedra.
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