Prerequsite: Background in Linear Algebra
Learning objectives
This course concentrates on recognizing and solving convex optimization problems that arise in Applications.
Learning outcome
At the end of the course student will be able to define appropriate optimization problem for a given practical problem. Student will be able to implement code and solve an optimization problem using MATLAB and CVX.
Syllabus
Introduction: convex sets, functions, basics of convex analysis, [2 lectures]
Relevant Optimization Concepts and Methods: Constrained vs. Unconstrained ;QP, LP and NLP, Combinatorial, Stochastic and Semi-definite optimization algorithms; Min-Max algorithms; Extreme point analysis, saddle point method. Chance constrained program. (8lectures)
Unconstrained Optimization and Multi Dimensional Gradient Methods :Steepest-Descent, Conjugate- Gradient, Newton, Quasi-Newton, Sub-Gradient,(4lectures)
Few Selected Topics from following list: (4lectures)
Stochastic Gradient descent, Proximal methods, Accelerated Proximal methods, ADMM, convex optimization for big data, interior-point methods; Constrained Optimization: Lagrange Multiplier, Karush Kuhn Tucker (KKT) conditions, First-Order and Second-Order Necessary Conditions for minima and maxima; (4lectures)
Few Selected Topics from following list: (4lectures)
Duality Theory. Project Gradient, L*-norms; Multiple kernel Method, penalty barrier methods Application: signal processing, statistics and machine learning, control and mechanical engineering, digital and analog circuit design and finance. (4 lectures)
Textbooks
- Convex Optimization, Stephen Boyd and LievenVandenberghe Paperback Cambridge India (2016) ISBN-13:978-1316603598/1316603598
- Practical Methods of Optimization 2ndEdition Paperback, Wiley India(2017) ISBN-13:978-8126567904/8126567902
References
- Convex Optimization Theory,1st Edition, Dimitri P. Bertsek, Paperback Universities Press, @2010, ISBN-13::978-8173717147/8173717141
- Convex Optimization Algorithm, 1st Edition , Dimitri P. Bertsek, Universities Press, @2010,ISBN-13:978-1886529281/1886529280
Past Offerings
- Offered in Jan-May, 2018 by Sahely
Course Metadata
| Item | Details |
|---|---|
| Course Title | Convex Optimization |
| Course Code | CS4502 |
| Course Credits | |
| Course Category | PME |
| Approved on | Senate of IIT Palakkad |
| Course status | old |