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)

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

1. Convex Optimization, Stephen Boyd and LievenVandenberghe Paperback Cambridge India (2016) ISBN-13:978-1316603598/1316603598
2. Practical Methods of Optimization 2ndEdition Paperback, Wiley India(2017) ISBN-13:978-8126567904/8126567902

# References

1. Convex Optimization Theory,1st Edition, Dimitri P. Bertsek, Paperback Universities Press, @2010, ISBN-13::978-8173717147/8173717141
2. 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