Global Optimization of Polynomials
نویسنده
چکیده
Recall we were considering the problem minz∈Rn p(z) where p(z) is a degree 2m polynomial such that p(z) = ∑ |α|≤2m pαz , where α = (α1, . . . , αn) is a vector of exponents, using the notation that z = z1 1 . . . z αn n . One equivalent way of expressing this problem is to notice this is the same as minimizing ∫ p(z)μ(dz) over the set of all probability distributions μ and note that it’s equivalent to consider only the first 2m moments of μ.
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