A quantum algorithm solves SOCPs with O~(√r γ^5 + √m γ^4) queries and a classical algorithm uses O~(n γ^4 + m γ^6) samples, nearly matching LP complexity.
DSOS and SDSOS optimization: More tractable alternatives to sum of squares and semidefinite optimization
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Quantum and classical algorithms for SOCP based on the multiplicative weights update method
A quantum algorithm solves SOCPs with O~(√r γ^5 + √m γ^4) queries and a classical algorithm uses O~(n γ^4 + m γ^6) samples, nearly matching LP complexity.