Two restart-free accelerated first-order methods for nonconvex functions with Lipschitz gradients and Hessians achieve O(ε^{-7/4}) complexity by discretizing a new ODE model, with adaptive Lipschitz estimation in one variant.
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2026 2verdicts
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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.
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A Restart-Free Accelerated Algorithm for Non-Convex Minimization: Continuous and Discrete Analysis
Two restart-free accelerated first-order methods for nonconvex functions with Lipschitz gradients and Hessians achieve O(ε^{-7/4}) complexity by discretizing a new ODE model, with adaptive Lipschitz estimation in one variant.
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A survey of trust-region radius update mechanisms. Part I: First-order analysis
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.