Convex Analysis and Optimization

Conic programming: linear programming (LP), second-order cone programming (SOCP), semidefinite programming (SDP), linear matrix inequalities, conic duality, conic duality theorem, Applications of semidefinite programming: control and system theory, combinatorial and nonconvex optimization, machine learning, Smooth convex optimization: gradient descent, optimal first-order methods (Nesterov's method and its variants), complexity analysis, Nonsmooth convex optimization: conjugate functions, smooth approximations of nonsmooth functions by conjugation, prox-functions, Nesterov's method for composite functions, Proximal minimization and mirror-descent algorithms (MDA),Augmented Lagrangian methods and alternating direction method of multipliers (ADMM),Example problems in statistics, signal and image processing, control theory.