The goal is to introduce students with the basics of convex optimization through relevant applications, techniques for formulating and solving optimization problems, and software tools for convex optimization. An important part of the course is a course project in which the students will independently work through all the described phases of solving an optimization problem, for a given practical application. Every student will be given an opportunity to choose a topic for the course project by his/her free choice, while the final project goal will be defined in collaboration with the course intructor. The students will also be given a set of modern optimization problems from the areas of communications (networking, point-to-point) and signal processing, in which they could also choose the topic for the course project.

After successful completion of the course, students will be able to formulate a given design problem as a mathematical optimization problem, cast it as a convex optimization problem (if necessary, by applying an appropriately chosen convex reformulation or relaxation), and solve it using the corresponding software tools.

- matrix algebra (fundamental vector subspaces, EVD, SVD, etc.) - methodology for casting design problems as mathematical optimization - convex analysis (convex sets, convex functions) - types of convex optimization problems (linear, quadratic, second order cone, SDP) with accompanying examples - nonconvex optimization problems and their convex relaxations/reformulations with accompanying examples - optimization algorithms (gradient descent, Newton) - software tools for convex optimization (cvx)

lectures, recitations, software training