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math.OC2024
Some Primal-Dual Theory for Subgradient Methods for Strongly Convex Optimization
Benjamin Grimmer, Danlin Li
We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of…
math.OC2024
A Strengthened Conjecture on the Minimax Optimal Constant Stepsize for Gradient Descent
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Drori and Teboulle [4] conjectured that the minimax optimal constant stepsize for N steps of gradient descent is given by the stepsize that balances performance on Huber and quadra…
math.OC2024
Accelerated Objective Gap and Gradient Norm Convergence for Gradient Descent via Long Steps
Benjamin Grimmer, Kevin Shu, Alex L. Wang
This work considers gradient descent for L-smooth convex optimization with stepsizes larger than the classic regime where descent can be ensured. The stepsize schedules considered…