This paper isolates admissibility conditions for trust-region radius updates that guarantee first-order stationarity and O(ε^{-2}) complexity, verifies them across five mechanism classes, and extends prior frameworks with new convergence results under linear Hessian growth.
The conjugate gradient method and trust regions in large scale optimization
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A Riemannian optimization method on fixed-rank matrix manifolds computes low-rank approximations to the solutions of parametrized systems, extending from linear to nonlinear cases with theoretical support for low-rank structure and preconditioning strategies.
SciPy 1.0 documents a mature open-source library that has become the de facto standard for scientific algorithms in Python with broad adoption across research projects.
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Low-rank solutions to a class of parametrized systems using Riemannian optimization
A Riemannian optimization method on fixed-rank matrix manifolds computes low-rank approximations to the solutions of parametrized systems, extending from linear to nonlinear cases with theoretical support for low-rank structure and preconditioning strategies.