A two-step negative curvature method is extended to deterministic and stochastic noisy settings with second-order convergence guarantees, plus a practical adaptive-sampling Newton-CG variant.
Topology optimization: theory, methods, and applications
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Exploiting Negative Curvature in Conjunction with Adaptive Sampling: Theoretical Results and a Practical Algorithm
A two-step negative curvature method is extended to deterministic and stochastic noisy settings with second-order convergence guarantees, plus a practical adaptive-sampling Newton-CG variant.