EE5121 : Convex Optimization
Time and Place
C slot,CRC 103
Office hours
Wednesday 3-4 pm
Teaching Assistants
- Satya Jayadev Pappu, ee15d202@ee.iitm.ac.in
- Kiran Rokade, ee17s011@smail.iitm.ac.in
- Ramaseshan, ee17d402@smail.iitm.ac.in
- Vijayanand, ee17s046@smail.iitm.ac.in
- Siva Shanmugam, ee17s024@smail.iitm.ac.in
- Aathira Prasad, ee18s033@smail.iitm.ac.in
Neema Davis, ee14d212@ee.iitm.ac.in
Grading
- CVX assignment- 10%
- Mid-sem - 30%
- End-sem - 40%
- Tutorial quiz - 20%
Tutorials
Tutorial questions would be uploaded on Moodle. There would a tutorial session for each tutorial conducted mostly during the Friday lecture hour.
Pre-requisites
Basics of linear algebra
Learning Outome
- To recognize and formulate convex optimization problems
Course Contents
- Mathematical preliminaries: real analysis - ordered sets, metric spaces, norm, inner product, open, closed and compact sets, continuous and differentiable functions
- Convex sets: Standard examples of convex sets, operations preserving convexity, separating and supporting hyperplane, generalized inequalities
- Convex functions: First and second order conditions for convexity, examples, operations preserving convexity, quasiconvex functions, logconcave functions
- Convex optimization problems: Standard form, equivalent formulation, optimality criteria, quasi convex optimization, linear programming, quadratic programming, cone programming, SDPs, LMIs, geometric programming, Multi-objective optimization
- Duality: Lagrangian duality, weak and strong duality, slater's condition, optimality condition, complementary slackness, KKT conditions
- Some basic algorithms (if time permits)
Reference Material
- Convex optimization by Stephen Boyd and Lieven Vandenberghe
- Lectures on Modern Convex Optimization by Aharon BenTal and Arkadi. Nemirovski
- Convex Optimization Theory by Dimitri P. Bertsekas
- (Real analysis) Principles of Mathematical analysis by Walter Rudin (3rd edition)
- (Linear algebra)Linear Algebra and its Applications by Gilbert Strang (4th edition)