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math.OC2026
Introduction to stochastic gradient methods
Simon Weissmann
These lecture notes provide an introduction to first-order optimization methods with a particular emphasis on stochastic gradient methods. We begin with deterministic gradient base…
math.OC2026
Polyak's Heavy Ball Method Achieves Accelerated Local Rate of Convergence under Polyak-Lojasiewicz Inequality
Sebastian Kassing, Simon Weissmann
In this work, we analyze the convergence of Polyak's heavy ball method in both continuous and discrete time for non-convex -objective functions satisfying the Polyak-Lojasiewi…
math.OC2025
Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularization
Sebastian Kassing, Simon Weissmann, Leif Döring
The present article studies the minimization of convex, L-smooth functions defined on a separable real Hilbert space. We analyze regularized stochastic gradient descent (reg-SGD),…