Subject Code: MA7L023 Subject Name:  Convex Analysis and Optimization L-T-P: 3-1-0 Credit:4
Pre-requisite(s): Optimization Techniques(MA5L013)
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.
Text Books:
  1. Boyd S. and Vandenberghe L. Convex Optimization, Cambridge University Press
  2. Bertsekas D. Nonlinear Programming, Athena Scientific
Reference Books:
  1. Ben-Tal A. and Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization
  2. Nesterov Y. Introductory Lectures on Convex Optimization: A Basic Course, Kluwer Academic Publisher
  3. Bertsekas D., Nedic A., and Ozdaglar A. Convex Analysis and Optimization, Athena Scientific