6 papers
Performance Estimation for Smooth and Strongly Convex Sets
Alan Luner, Benjamin Grimmer
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured se…
Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets
Ning Liu, Benjamin Grimmer
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much…
Composing Optimized Stepsize Schedules for Gradient Descent
Benjamin Grimmer, Kevin Shu, Alex L. Wang
Recent works by Altschuler and Parrilo and the authors have shown that it is possible to accelerate the convergence of gradient descent on smooth convex functions, even without mom…
On Averaging and Extrapolation for Gradient Descent
Alan Luner, Benjamin Grimmer
This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather t…
First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points
Zhichao Jia, Benjamin Grimmer
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we sh…
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…