Conic programming: linear programming (LP), secondorder 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 firstorder methods (Nesterov's method and its variants), complexity analysis, Nonsmooth convex optimization: conjugate functions, smooth approximations of nonsmooth functions by
conjugation, proxfunctions, Nesterov's method for composite functions, Proximal minimization and mirrordescent algorithms (MDA),Augmented Lagrangian methods and alternating direction method of multipliers (ADMM),Example problems in statistics, signal and image processing, control theory. 
Reference Books:
 BenTal A. and Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPSSIAM Series on Optimization
 Nesterov Y. Introductory Lectures on Convex Optimization: A Basic Course, Kluwer Academic Publisher
 Bertsekas D., Nedic A., and Ozdaglar A. Convex Analysis and Optimization, Athena Scientific
