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Gradient descent can adapt to exploding curvature without expensive linesearches or global Lipschitz smoothness, unifying normalized and hyperbolic updates under a single, locally adaptive framework.
Second-order Frank鈥揥olfe optimization is no longer handcuffed to polytopes: damped Newton subproblems coupled with residual backtracking unlock global linear and local quadratic convergence across general compact convex sets.
Accelerated Bregman proximal gradient methods can achieve optimal $\mathcal{O}(k^{-2})$ convergence without the restrictive triangle-scaling conditions that have historically throttled non-Euclidean first-order optimization.
