Frank-Wolfe Algorithm in Python

Le Anh DUNG and Paul MELKI (Toulouse School of Economics)

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Implementation of the Frank-Wolfe optimization algorithm in Python with an application for solving the LASSO problem.

Some useful resources about the Frank-Wolfe algorithm can be found here:

• http://fa.bianp.net/blog/2018/notes-on-the-frank-wolfe-algorithm-part-i/
• https://people.csail.mit.edu/stefje/fall15/notes_lecture14.pdf
• https://www.stat.cmu.edu/~ryantibs/convexopt/lectures/frank-wolfe.pdf

This implementation is divided over two files:

• frank_wolfe.py: in this file we define the functions required for the implementation of the Frank-Wolfe algorithm, as well as the function frankWolfeLASSO which solves a LASSO optimization problem using the algorithm.
• implementation_LASSO.py: in this file we solve different LASSO problems using our implementation, which allows to look at the sensitivity of the algorithm towards different changes in the problem's definition: for example, changes in the number of observations (n), or the number of parameters (p).

This code has been developed as part of the final project for the course Optimization for Big Data in M1 Statistics and Econometrics at Toulouse School of Economics.