We are interested in efficient algorithms for solving optimization problems with L0 (sparsity) constraints. For instance, consider the sparse linear regression problem: basically standard least squares but with fewer data-points than the dimension.
One of the algorithms for this is to alternatingly perform a gradient descent step and a thresholding step. This is called Iterative Hard Thresholding (IHT). We propose a new algorithm for IHT which performs accelerated gradient descent instead of vanilla gradient descent. We are looking to prove guarantees for this algorithm.
Unfortunately our manuscript is still private. Please email me if you would like to have a look or discuss.