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math.OC2025
Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms
Christopher Criscitiello, Jungbin Kim
Geodesic convexity (g-convexity) is a natural generalization of convexity to Riemannian manifolds. However, g-convexity lacks many desirable properties satisfied by Euclidean conve…
math.OC2025
A Proof of Exact Convergence Rate of Gradient Descent. Part I. Performance Criterion
Jungbin Kim
We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization, with respect to the performance criterion $\Vert \nabla f(x_N)\Vert^2/(f…
math.OC2025
A Proof of the Exact Convergence Rate of Gradient Descent
Jungbin Kim
We prove the exact worst-case convergence rate of gradient descent for smooth strongly convex optimization on . Concretely, assuming that the objective function i…