Introduces APS, an adaptive proximal method achieving O(ε^{-2}) iteration complexity for ε-stationary points of ρ-weakly convex functions with unknown ρ in deterministic and stochastic settings.
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math.OC 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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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Adaptive Proximal Methods for Weakly Convex Optimization with Unknown Parameter: Deterministic and Stochastic Guarantees
Introduces APS, an adaptive proximal method achieving O(ε^{-2}) iteration complexity for ε-stationary points of ρ-weakly convex functions with unknown ρ in deterministic and stochastic settings.
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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.