L1TestPack has just been updated to version 1.1. With the help of Andreas Tillmann I enhanced this small gadget for issues related to minimization. New functions are

- Routines to directly calculate a source element for a given matrix and a vector , that is, calculate a vector such that
The existence of such a vector ensures that the minimization problem (the Basis Pursuit problem)

has the unique solution (is other words: is recovered exactly). This is particularly helpful is you are interested in unique solutions for Basis pursuit without posing strong conditions which even imply –-equivalence.

- Routines related to RIP constants, the ERC coefficient of Joel Tropp and the mutual coherence.
- An implementation of the heuristic support evaluation HSE (also described in my previous post). (By the way: We were tempted to call this device “support evaluation routine” with acronym SuppER but abandoned this idea.)

November 2, 2011 at 4:49 pm

[…] solutions to underdetermined systems is -minimization a.k.a. Basis Pursuit on which I blogged recently: […]

August 20, 2012 at 5:51 pm

[…] My own talk was the third and last one in that session. I talked about the issue of constructing test instance for Basis Pursuit Denoising. I argued that the naive approach (which takes a matrix , a right hand side and a parameter and let some great solver run for a while to obtain a solution ) may suffer from “trusted method bias”. I proposed to use “reverse instance construction” which is: First choose , and the solution and the construct the right hand side (I blogged on this before here). […]