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07/24/2023
Open Problem: Polynomial linearly-convergent method for geodesically convex optimization?
Let f ℳ→ℝ be a Lipschitz and geodesically convex function defined on a d...
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06/05/2023
Curvature and complexity: Better lower bounds for geodesically convex optimization
We study the query complexity of geodesically convex (g-convex) optimiza...
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07/07/2022
The effect of smooth parametrizations on nonconvex optimization landscapes
We develop new tools to study the landscapes of nonconvex optimization p...
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11/25/2021
Negative curvature obstructs acceleration for geodesically convex optimization, even with exact first-order oracles
Hamilton and Moitra (2021) showed that, in certain regimes, it is not po...
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07/08/2021
Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy
We consider the problem of provably finding a stationary point of a smoo...
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01/10/2021
Random Conical Tilt Reconstruction without Particle Picking in Cryo-electron Microscopy
We propose a method to reconstruct the 3-D molecular structure from micr...
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11/06/2020
Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates
Quasi-Newton techniques approximate the Newton step by estimating the He...
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08/05/2020
An accelerated first-order method for non-convex optimization on manifolds
We describe the first gradient methods on Riemannian manifolds to achiev...
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07/02/2019
The generalized orthogonal Procrustes problem in the high noise regime
We consider the problem of estimating a cloud of points from numerous no...
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06/10/2019
Efficiently escaping saddle points on manifolds
Smooth, non-convex optimization problems on Riemannian manifolds occur i...
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05/08/2019
Multi-target Detection with an Arbitrary Spacing Distribution
Motivated by the structure reconstruction problem in cryo-electron micro...
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03/12/2019
Multi-target detection with application to cryo-electron microscopy
We consider the multi-target detection problem of recovering a set of si...
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09/29/2018
Toward single particle reconstruction without particle picking: Breaking the detection limit
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X...
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06/11/2018
Smoothed analysis of the low-rank approach for smooth semidefinite programs
We consider semidefinite programs (SDPs) of size n with equality constra...
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03/01/2018
Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form
Semidefinite programs (SDP) are important in learning and combinatorial ...
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10/23/2017
3D ab initio modeling in cryo-EM by autocorrelation analysis
Single-Particle Reconstruction (SPR) in Cryo-Electron Microscopy (cryo-E...
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06/01/2015
A Riemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints
We propose a new algorithm to solve optimization problems of the form f...
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08/23/2013