The latest "News and Views" issue from SIAM's Group on Optimization just came out. The issue highlights Alex Wang, Kevin Shu, and my work on "subgame perfect" algorithm design. These algorithms use game theory ideas to describe the best way for algorithms to adapt at runtime 1/4

I'm excited to share some joint work done with TaeHo Yoon. We considered algorithm design for fixed-point problems. This area models gradient descent, minimax optimization, and more. Below, I give the wild ride of this paper. Mathematically, it is gorgeous.

Last year, Mateo Diaz and Ian McPherson began searching for provably good nonsmooth optimization methods on manifolds. Oh boy, did I quickly learn the hard subtleties of numerical work on manifolds, especially combined with finicky subgradients.

📚 New Arxiv Paper Title: Nonsmooth Riemannian optimization with inexact manifold primitives via bundle methods Authors: Mateo D\'iaz, Benjamin Grimmer, Ian McPherson Read more: https://arxiv.org/abs/2604.27078

For a decade it was open whether Frank-Wolfe's O(1/√ε) rate on strongly convex sets is tight. We show it is: Ω(1/√ε), even for a simple quadratic on a unit ball.

For the second morning this week, one of my phd students defended (successfully!) 🎉🎓🎉 Today, Alan Luner defended his excellent work, "On Large-Scale Optimization: Optimal Methods and Computer-Assisted Algorithm Design". I promise this is the last such announcement for the year

This morning my PhD student Thabo Samakhoana defended his thesis (successfully!) 🎉🎓🎉 Was a great five years working with him towards his thesis "On Optimal Smoothings and their Applications to Optimization and Deep Learning"

This paper generated me new office decorations as well. Below is the strongly convex set we designed that is provably hard for all Frank-Wolfe methods (at least for two steps). The paper builds this "evil" shape in d dimensions able to counteract any d/2 step method

Ben Grimmer@profgrimmer.bsky.social · 5mo ago

For anyone interested in our lower bound result for Frank-Wolfe methods in Nemirovski and Yudin "zero-chain" lower bounding style, a link: arxiv.org/abs/2602.22608

A small digression on something I find strange in accelerated convex optimization theory: Since the 80s, in unconstrained minimization by gradient methods, smoothness is known to allow a fast O(1/T^2) convergence rate by Nesterov. Nemirovski and Yudin give matching lower bounds.

Lately, non-crossing partitions have shown up out of nowhere in my research, which have a lovely duality structure. This inspired some good art and fractals :) Wanted to share the fun here (just sharing the pretty art for now, the research story will come in due time) 1/4

Happy to announce that my work "On optimal universal first-order methods for minimizing heterogeneous sums" just received the Optimization Letters Best Paper Prize. link.springer.com/journal/1159... This work is part of a larger trend, fighting the brittleness of classic smooth/nonsmooth models.

Optimization Letters

Optimization Letters covers all aspects of optimization, including theory, algorithms, computational studies, and applications. This journal provides an ...

link.springer.com

Sunday morning spent setting up my office in the new @hopkinsdsai.bsky.social building. I gained a good amount more wall space, so I have the freedom to grow my collections again

Join us in advancing data science and AI research! The Johns Hopkins Data Science and AI Institute Postdoctoral Fellowship Program is now accepting applications for the 2026–2027 academic year. Apply now! Deadline: Jan 23, 2026. Details and apply: apply.interfolio.com/179059

My student Thabo Samakhoana and I have been obsessed with smoothings lately. The softmax/logSumExp smoothing seems to be the standard everywhere in ML and optimization. So, in what sense is this choice "optimal"? We found some "elementary" answers, both good and bad news (1/4)

A new paper out with TaeHo Yoon and Ernest Ryu: We looked at the design of optimal fixed-point algorithms. That is, seeking to approximately solve T(y)=y using as few evaluations of the operator T() as possible. Maximally efficient methods are "minimax optimal" 1/

Lately, I have been obsessed with developing theoretically based optimization algorithms that actually attain the best practical performance. Alas, the classic model of minimax optimal methods is overly conservative; it overfits to tune its worst-case. We found a path forward 1/

Enjoyed being part of the Brin Mathematical Research Center's summer school on Scientific Machine Learning last week. Many very good talks and always nice to visit UMD!

📢 Excited to share a new paper with PhD student Thabo Samakhoana. Nonsmooth optimization often uses smoothings, nearby smooth functions or sets. Often chosen in an ad hoc fashion. We do away with ad hoc, characterizing optimal smoothings for convex cones and sublinear functions

Oh, that’s so satisfying! I stopped at the 4-norm ball thinking I had the solution as it fits the hole like a pot lid (has a perfect circle as an intersection).

Yesterday I posted a maths puzzle that AIs all failed at (thanks for running the premium versions @xy-han.bsky.social and Ernest Ryu). The puzzle just needs elementary reasoning about p-norm balls (third row on my shelf below). This thread gives the puzzle, solution, and a 3D printed demo :)

Ben Grimmer@profgrimmer.bsky.social · last yr.

I've invented a simple, lovely math puzzle I expect every AI fails: Suppose you're a mathematical sailor at sea on a boat that has a perfectly cylindrical hole in the floor. All you brought is a collection of every p norm ball except p=2 (drat!). What do you do to cork the hole and save yourself?

I've invented a simple, lovely math puzzle I expect every AI fails: Suppose you're a mathematical sailor at sea on a boat that has a perfectly cylindrical hole in the floor. All you brought is a collection of every p norm ball except p=2 (drat!). What do you do to cork the hole and save yourself?

very cool talk: youtu.be/K_dhTP2I2uo?... "Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm" - Jason Altschuler

Jason Altschuler - Near-Linear Runtime for a Classical Matrix Preconditioning Algorithm

YouTube video by Institute for Pure & Applied Mathematics (IPAM)

youtu.be

Lots of great questions and engagement from Wisconsin folk! They were quick at turning around and getting it online. See below: www.youtube.com/watch?v=QNfq...

Ben Grimmer - "Optimizing Optimization Methods, To and Beyond Minimax Optimality"

YouTube video by UWMadison SILO Seminar

youtube.com

Ben Grimmer@profgrimmer.bsky.social · last yr.

Just landed in Madison! Tomorrow, I'll be sharing my work optimizing optimization methods, to and beyond minimax optimality in their SILO seminar. Will share a link to the talk on YouTube after

Just landed in Madison! Tomorrow, I'll be sharing my work optimizing optimization methods, to and beyond minimax optimality in their SILO seminar. Will share a link to the talk on YouTube after

The optimization technique of gradient descent is like feeling your way down a mountain in the dark. You may not be able to see the way, but you’ll eventually reach the lowest point in the area. (From the archive) www.quantamagazine.org/risky-giant-...

My PhD students are awesome. They gave my fiancee(wife) and I this gorgeous cherry blossom card for our wedding and soon honeymoon in Japan <3

As an early wedding present (happening this Saturday!), my dad made me a custom shelf to hold my collection of unit norm balls! Rockafellar+Wets's thick textbook is included for reference.

New (first) paper with my student Aaron Zoll :) We consider first-order methods for a ridiculously general model: minimizing a convex composition of functions g_j(x) that vary heterogeneously in whether they are smooth, nonsmooth, convex, strongly convex or anything in between.

🎉Congrats to the 126 early-career scientists who have been awarded a Sloan Research Fellowship this year! These exceptional scholars are drawn from 51 institutions across the US and Canada, and represent the next generation of groundbreaking researchers. sloan.org/fellowships/...

PhD students set up arts and crafts to make Valentine's mailboxes and collect cards. They (slide) rule :)