Tuesday, July 07, 2015

Manopt 2.0: A Matlab tool­box for opti­mization on manifolds - implementation -

Nicolas Boumal just let me know of the following:

Dear Igor,

Bamdev (cc) and I develop Manopt, a Matlab toolbox for optimization on manifolds.

You featured a nice post about it on Nuit Blanche on May 28, 2013:

Over the last two years, the toolbox has improved vastly, in part thanks to our great contributors, and we just released Manopt 2.0 yesterday: 

We would be delighted if you could announce this major release on your blog once again.

Manopt is a toolbox for optimization on manifolds, that is, on smooth nonlinear spaces. This is ideal to handle rank constraints and orthogonality constraints, to name a few, with major applications in large-scale machine learning, computer vision, numerical linear algebra and scientific computing. Generically, it is an excellent paradigm to handle symmetry and invariance in optimization. Of course, Manopt can also optimize over linear spaces (and it's quite good at it). It is also a powerful way to refine ballpark estimates obtained from relaxations.

The toolbox is user friendly, requiring little knowledge about manifolds to get started. See our tutorial and the many examples in the release: 

For a brief overview of what optimization on manifolds is about, this blog post may be a good start:

We hope you may find this to be of interest for Nuit Blanche's readership.

Thank you for your time,

Sure thing Nicolas and Bamdev !

From the About page:

We see a growing number of papers in various disciplines where researchers use Manopt. A list is available on Google Scholar. We single out a few projects we think illustrate some of the flexibility of the toolbox:
  • Artiom Kovnatsky, Klaus Glashoff and Michael M. Bronstein proposed MADMM: a generic algorithm for non-smooth optimization on manifolds. This is essentially ADMM, where one of the steps is smooth optimization on a manifold ; that step is performed using Manopt.
  • Reshad Hosseini and Suvrit Sra released a paper entitled Manifold Optimization for Gaussian Mixture Models. They address the important problem of estimating the distribution of data, when it is assumed to be sampled from a mixture (linear combination) of Gaussian distributions. See their MixEst project page for code and more. The same authors also developed the Geometric Optimization Toolbox (GOPT), aimed at optimization over the manifold of positive definite matrices. This includes a Riemannian BFGS algorithm.
  • Vris Yuen-Lam Cheung, Dmitriy Drusvyatskiy, Nathan Krislock and Henry Wolkowicz consider a sensor network localization problem. They propose a smart way of obtaining a cheap initial guess, then refine this ballpark estimate to high accuracy with Manopt. They find that neither works very well without the other. The general idea of combining smart spectral or convex formulations to obtain rough (but controllable) estimates, then refining these using Manopt, is successful in many applications.
but also 

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