Lieven Vandenberghe University of California, Los Angeles (UCLA) EE Part one of this tutorial will cover the basics of convex analysis, focusing on results that are most relevant for convex modeling (i.e. recognizing and formulating convex optimization problems in applications) and for large-scale algorithms (duality theory, subgradients, proximal operators). Part two will give an introduction to first-order algorithms, including recent developments in the area of proximal gradient methods, and alternating minimization and splitting algorithms.