A new sequential cubic programming algorithm for equality-constrained optimization achieves O(ε_g^{-3/2}) complexity for the Lagrangian gradient, O(ε_H^{-3}) for second-order stationarity, and O(ε_c^{-1}) for constraint violation, claimed as the best known rates.
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A Sequential Cubic Programming Method with Second-Order Complexity Guarantees for Equality Constrained Optimization
A new sequential cubic programming algorithm for equality-constrained optimization achieves O(ε_g^{-3/2}) complexity for the Lagrangian gradient, O(ε_H^{-3}) for second-order stationarity, and O(ε_c^{-1}) for constraint violation, claimed as the best known rates.