Trust-Region Method
A classical numerical optimization technique that defines a trusted neighborhood around the current iterate, approximates the objective with a quadratic model within that region, and dynamically adjusts the region radius based on the ratio of actual to predicted decrease in the objective function.
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The paper systematically extends the classical trust-region method from numerical optimization to Wasserstein measure spaces for minimizing smooth potential-interaction energies.
The method reaches an ε-stationary point within O(ε⁻²) outer trial steps (including rejected trials), a complexity order consistent with the results of trust-region methods in classical non-convex optimization.
Compared to purely first-order Wasserstein gradient flow methods, the trust-region framework provides explicit control over the reliability of local approximations and is more robust in non-convex energy landscapes
All Facts (3)
The paper systematically extends the classical trust-region method from numerical optimization to Wasserstein measure spaces for minimizing smooth potential-interaction energies.
50%UnverifiedThe method reaches an ε-stationary point within O(ε⁻²) outer trial steps (including rejected trials), a complexity order consistent with the results of trust-region methods in classical non-convex optimization.
50%UnverifiedCompared to purely first-order Wasserstein gradient flow methods, the trust-region framework provides explicit control over the reliability of local approximations and is more robust in non-convex energy landscapes
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