I have updated my research pages with an entry on Sparse Function Minimization. This is the result of very exciting recent work with Bhiksha Raj and Sohail Bahmani. We have generalized CoSaMP to solve (exactly or approximately) the  problem

We call this algorithm the Gradient Support Pursuit (GraSP). I tried to include figures describing the algorithm in a simple way and demonstrating the similarities to CoSaMP; let me know if I didn’t do a good job! Our theory guarantees the accuracy of the solution based on the Stable Restricted Hessian (SRH) and the Stable Restricted Linearization (SRL), two properties we defined that generalize the RIP. For more details follow the link!