Abstract:In this paper, we analyze the bit complexity of deciding whether a given polynomial can be represented as a sum of squares of polynomials. We show that the weak membership problem for the sum-of-squares cone lies in $\mathrm{P}$. Furthermore, we give a polynomial-time algorithm which computes, for a given polynomial and positive parameter $\epsilon$, an $\epsilon$-relaxed closest sum-of-squares polynomial.
From: Victor Magron [view email]
[v1]
Tue, 23 Jun 2026 19:45:04 UTC (796 KB)
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