From the 1 of 11 linked papers with an AI index.
11 papers
Implicit Primal-Dual Guarantees in Unconstrained First-Order Minimization
Benjamin Grimmer, Alex L. Wang
This work considers the design of first-order convex optimization algorithms and convergence proofs. In particular, we consider nonsmooth Lipschitz and smooth problems accessed thr…
Lower Bounds for Linear Minimization Oracle Methods Optimizing over Strongly Convex Sets
Benjamin Grimmer, Ning Liu
The paper establishes lower bounds on the number of iterations required by deterministic linear minimization oracle methods, such as Frank‑Wolfe, to solve smooth strongly convex op…
A Theory of Composition and Duality of Extremal Optimal Fixed-Point Algorithms
TaeHo Yoon, Benjamin Grimmer
In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extre…
Nonsmooth Riemannian optimization with inexact manifold primitives via bundle methods
Mateo DÃaz, Benjamin Grimmer, Ian McPherson
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel…
Beyond Minimax Optimality: A Subgame Perfect Gradient Method
Benjamin Grimmer, Kevin Shu, Alex L. Wang
The study of convex optimization has historically been concerned with worst-case convergence rates. The development of the Optimized Gradient Method (OGM), due to \citet{drori2012P…
A Practical Adaptive Subgame Perfect Gradient Method
Alan Luner, Benjamin Grimmer
We present a performant gradient method for smooth convex optimization, drawing inspiration from several recent advances in the field. Our algorithm, the Adaptive Subgame Perfect G…