Surprisingly many real-world optimization problems can be reformulated as convex optimization problems.
This convexity plays a central role in the computational tractability of a solution.
The goals of this course are
(i) to provide the students with the necessary background to recognize optimization that can be reformulated as convex ones;
(ii) to study the duality theory of convex optimization from the point of view of conic programming, which includes as particular cases the linear programming (LP), semidefinite programming (SDP), second order cone programming (SOCP), and geometric programming (GP);
(iii) to review a variety of applications of convex optimization from various branches such as engineering, control theory, data fitting, statistics and machine learning;
(iv) finally, to understand algorithms for convex programming, in particular interior point methods, and to be able to use modern interfaces to pass optimization problems to solvers that implement these algorithms.