We will discuss practical optimization algorithms for estimating sparse models, both from a statistics and a signal processing point of view. First, we will cover non-convex optimization techniques such as greedy algorithms and DC-programming. Second, we will focus on convex optimization: first-order methods, iterative reweighted least squares, and the homotopy method for the Lasso. References: [1] Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2012). Optimization with sparsity-inducing penalties.Foundations and Trends in Machine Learning, 4(1), 1--106, 2012. http://lear.inrialpes.fr/people/mairal/resources/pdf/ftml.pdf