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.


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)


  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


  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

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