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Found 9 papers, 3 papers with code
Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates
Quasi-Newton techniques approximate the Newton step by estimating the Hessian using the so-called secant equations.
Optimization and Control Numerical Analysis Numerical Analysis
Efficiently escaping saddle points on manifolds
Specifically, for an arbitrary Riemannian manifold $\mathcal{M}$ of dimension $d$, a sufficiently smooth (possibly non-convex) objective function $f$, and under weak conditions on the retraction chosen to move on the manifold, with high probability, our version of PRGD produces a point with gradient smaller than $\epsilon$ and Hessian within $\sqrt{\epsilon}$ of being positive semidefinite in $O((\log{d})^4 / \epsilon^{2})$ gradient queries.
Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction
In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations.
Smoothed analysis of the low-rank approach for smooth semidefinite programs
In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X = YY^*$ is the SDP variable.
Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications.
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue.
Optimization and Control Numerical Analysis
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 $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices.
Manopt, a Matlab toolbox for optimization on manifolds
Optimization on manifolds is a rapidly developing branch of nonlinear optimization.
RTRMC: A Riemannian trust-region method for low-rank matrix completion
We address the problem of recovering such matrices when most of the entries are unknown.
