Transforming High-Dimensional Optimization: The Krylov Subspace Cubic Regularized Newton Method’s Dimension-Free Convergence

Searching for efficiency in the complex optimization world leads researchers to explore methods that promise rapid convergence without the burdensome computational cost typically associated with high-dimensional problems. Second-order methods, such as the cubic regularized Newton (CRN) method, have been celebrated for their swift convergence. However, their application becomes less feasible as the problem’s dimensionality increases, […]

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