Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.
Oracle complexity of second-order methods for smooth convex optimization.Mathematical Programming, 178(1):327–360
2 Pith papers cite this work. Polarity classification is still indexing.
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Improved upper bound of Õ(ε^{-4/(3p+1)}) p-th order oracle complexity for convex-concave minimax problems via Monteiro-Svaiter acceleration, with matching lower bound Ω(ε^{-2/(3p-1)}).
citing papers explorer
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Higher-Order Derivatives Do Not Accelerate the Computation of Fixed Points
Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.
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Solving Convex-Concave Problems with $\tilde{\mathcal{O}}(\epsilon^{-4/(3p+1)})$ $p$th-Order Oracle Complexity
Improved upper bound of Õ(ε^{-4/(3p+1)}) p-th order oracle complexity for convex-concave minimax problems via Monteiro-Svaiter acceleration, with matching lower bound Ω(ε^{-2/(3p-1)}).