Local LMO is a new projection-free method that achieves the convergence rates of projected gradient descent for constrained optimization by using local linear minimization oracles over small balls.
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Introduces the Riemannian ball-proximal point method (RB-PPM) that minimizes geodesically convex functions over metric balls on Hadamard manifolds and proves quasi-Fejér monotonicity, finite termination under constant radii, and convergence when the sum of radii diverges.
Rescaled ASGD recovers convergence to the true global objective by rescaling worker stepsizes proportional to computation times, matching the known time lower bound in the leading term under non-convex smoothness and bounded heterogeneity.
A trust-region stabilized proximal point method enforces a displacement condition to achieve linear descent for general nonsmooth convex problems.
A smoothing moving balls approximation method is proposed for difference-of-convex optimization over nonlinear conic constraints, with iteration complexity for approximate KKT points and convergence analysis in the convex case.
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Local LMO: Constrained Gradient Optimization via a Local Linear Minimization Oracle
Local LMO is a new projection-free method that achieves the convergence rates of projected gradient descent for constrained optimization by using local linear minimization oracles over small balls.