5 papers
A Complete Characterization of Optimal Subgradient Methods for Lipschitz Convex Minimization
Aaron Zoll, Benjamin Grimmer
We consider the design of optimal fixed-step first-order methods for -Lipschitz convex optimization given . Prior works have identified several distinct f…
An Elementary Proof of the Near Optimality of LogSumExp Smoothing
Thabo Samakhoana, Benjamin Grimmer
We consider the design of smoothings of the (coordinate-wise) max function in in the infinity norm. The LogSumExp function provides a c…
Inexactly Smooth Performance Estimation and New Optimized Gradient Methods
Aaron Zoll, Benjamin Grimmer
We consider a general class of ``inexactly smooth'' convex functions, providing a universal model capturing as special cases -smooth, -Lipschitz, and Hölder smooth functions…
A Parameter-Free Restart Scheme with Only a Parallelizable Overhead
Yue Wu, Benjamin Grimmer
It is well-known that first-order methods can offer accelerated convergence rates in the presence of growth structures. Restarting schemes provide a general tool for such speed-ups…
The Optimal Smoothings of Sublinear Functions and Convex Cones
Thabo Samakhoana, Benjamin Grimmer
This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions,…