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09/14/2023
Acceleration by Stepsize Hedging I: Multi-Step Descent and the Silver Stepsize Schedule
Can we accelerate convergence of gradient descent without changing the a...
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05/23/2022
Low-Rank Univariate Sum of Squares Has No Spurious Local Minima
We study the problem of decomposing a polynomial p into a sum of r squar...
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06/04/2021
Kernel approximation on algebraic varieties
Low-rank approximation of kernels is a fundamental mathematical problem ...
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02/25/2021
Semidefinite Relaxations of Products of Nonnegative Forms on the Sphere
We study the problem of maximizing the geometric mean of d low-degree no...
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01/27/2021
Shortest Paths in Graphs of Convex Sets
Given a graph, the shortest-path problem requires finding a sequence of ...
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04/07/2020
Approximating Min-Mean-Cycle for low-diameter graphs in near-optimal time and memory
We revisit Min-Mean-Cycle, the classical problem of finding a cycle in a...
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04/06/2020
Random Osborne: a simple, practical algorithm for Matrix Balancing in near-linear time
We revisit Matrix Balancing, a pre-conditioning task used ubiquitously f...
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02/11/2020
Maximizing Products of Linear Forms, and The Permanent of Positive Semidefinite Matrices
We study the convex relaxation of a polynomial optimization problem, max...
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07/12/2018
Convergence Rate of Block-Coordinate Maximization Burer-Monteiro Method for Solving Large SDPs
Semidefinite programming (SDP) with equality constraints arise in many o...
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04/09/2016
Chordal networks of polynomial ideals
We introduce a novel representation of structured polynomial ideals, whi...
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11/05/2012