TFOCS: Templates for First-Order Conic Solvers

TFOCS (pronounced tee-fox) provides a set of Matlab templates, or building blocks, that can be used to construct efficient, customized sovlers for a variety of convex models, including in particular those employed in sparse recovery applications. It was conceived and written by Stephen Becker, Emmanuel J. Candès and Michael Grant.

Despite the name, TFOCS is not restricted to conic models.

More information about the software can be found in the paper and the users' guide.

TFOCS is jointly owned by CVX Research, Inc. and Caltech. As of October 2, 2013, it has been made freely available for both academic and commercial use under a BSD 3-Clause license, subject to requirements of attribution and non-endorsement, and a disclaimer of warranty contained therein.

TFOCS in the press

We were award the Beale-Orchard-Hays prize in 2015 for excellence in mathematical programming.

Downloading

The source code for TFOCS is now hosted on GitHub. Feel free to visit the GitHub page to browse the code or clone the repository. Direct download links for the latest versions are provided on the Releases page. The packages include the main program files, the documentation, the paper, and a number of examples and demos.

Documentation / Demos

The users' guide is included with the distribution, and available separately here.
Click here for a list of the functions included with TFOCS.
Several demonstrations are available here. Each demonstration includes the source code and data files needed to reproduce the results.

Paper

Templates for convex cone problems ith applications to sparse signal recovery
by S. Becker, E. Candès, and M. Grant.
Stanford University Technical Report, September 2010.
Published in Mathematical Programming Computation, Volume 3, Number 3, August 2011.

The most up-to-date mathematical description is Chapter 4 of Stephen Becker's thesis (2011) which is the same as the journal paper but recasts the framework to apply for conjugate functions, rather than conic duals, and thus extend the applicability.

In the spirit of reproducible research, we provide the source code and data (ZIP file, 9.7MB) used for the examples in the paper. You must have the TFOCS package installed to run these examples.

Abstract

This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic formulation of the problem; second, determine its dual; third, apply smoothing; and fourth, solve using an optimal first-order method. A merit of this approach is its flexibility: for example, all compressed sensing problems can be solved via this approach. These include models with objective functionals such as the total-variation norm, ||Wx||_1 where W is arbitrary, or a combination thereof. In addition, the paper also introduces a number of technical contributions such as a novel continuation scheme, a novel approach for controlling the step size, and some new results showing that the smooth and unsmoothed problems are sometimes formally equivalent. Combined with our framework, these lead to novel, stable and computationally efficient algorithms. For instance, our general implementation is competitive with state-of-the-art methods for solving intensively studied problems such as the LASSO. Further, numerical experiments show that one can solve the Dantzig selector problem, for which no efficient large-scale solvers exist, in a few hundred iterations. Finally, the paper is accompanied with a software release. This software is not a single, monolithic solver; rather, it is a suite of programs and routines designed to serve as building blocks for constructing complete algorithms.

Support

Please note that the authors of TFOCS generally cannot offer direct email assistance. We hope that the resources we have assembled here will address most users’ issues. If the documentation and demos are insufficient, please consider the following alternatives:

Community-driven support

For TFOCS-specific usage questions that are not caused by bugs, please consider posing your question on the CVX Forum, a free question and answer forum modeled in the style of StackExchange family of sites. As the name implies, the forum is also used for CVX, but TFOCS users are welcome to ask questions on this forum as well. The authors of TFOCS do visit this forum regularly. If you are an experienced TFOCS user, we would ask you to join us and offer answers to other TFOCS users’ questions.

For more general questions about optimization that are not specific to TFOCS, the CVX Forum is not the appropriate venue. Instead, we invite you to consider two other online forums: the Computational Science Stack Exchange (CompSci SE) and [OR Exchange](http://or- exchange.org/). CompSci SE covers a variety of computational science topics, including convex optimization. OR-Exchange is a Q&A site sponsored by INFORMS, an international society for professionals in operations research, management science, and analytics. Both communities include a number of active optimization experts.

Submitting bug reports

If you encounter a bug in TFOCS, or an error in the documentation, please submit an report on the GitHub issue tracker for TFOCS. In order for us to effectively evaluate a bug report, we will need the following information:

• The output of the tfocs_version command, which provides information about your operating system, your MATLAB version, and your TFOCS version. Just copy and paste this information from your MATLAB command window into your report.
• A description of the error itself. If TFOCS provided the error message, please copy the full text of the error output into the report.
• If it is at all possible, please provide us with a brief code sample and supporting data that reproduces the error. If that cannot be accomplished, please provide a detailed description of the circumstances under which the error occurred.

Mailing list

If you wish to be notified of new TFOCS releases, please join the google group mailing list. Note that this mailing list is for announcements only.

Contract support

For more in-depth support, you may purchase a support contract from one or more of the authors. Please contact [email protected] for more information.