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. (8 lectures)

UNCONSTRAINED OPTIMIZATION AND MULTIDIMENSIONAL GRADIENT METHODS: Steepest-Descent, Conjugate-Gradient, Newton, Quasi-Newton, Sub-Gradient, (4 lectures)

Few Selected Topics from following list : (4 lectures) 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; (4 lectures)

Few Selected Topics from following list : (4 lectures) 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)

Text books

  1. Convex Optimization, Stephen Boyd and Lieven Vandenberghe Paperback Cambridge India (2016) ISBN-13: 978-1316603598/1316603598

  2. Practical Methods of Optimization 2nd Edition Paperback , Wiley India (2017) ISBN-13: 978-8126567904/8126567902

#Refferenes

  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

Meta Data

  • Proposing Faculty : Dr Sahely Bhadra
  • Department / Centre : Computer Science and Engineering
  • Programme : B.Tech
  • Proposal Type: Old
  • Offerings