Course Co-ordinated by IIT Kanpur
 Coordinators IIT Kanpur

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This course will deal with the fundamentals of optimization theory and algorithms. This course will be delivered for a wide audience consisting of science and engineering students. Mathematically oriented business students will profit from it.

This course will stress on the basic theory of optimization of differentiable functions and also discuss in detail the important numerical algorithms to solve such problems.

Motivating examples will be provided throughout the course

 S. No. Lectures/ Topics 1 Basic facts about maxima and minima 2 Examples and modeling 3 Mathematical Prerequisites 4 Optimality conditions for Unconstrained Optimization 5 The Steepest Descent Method 6 Convergence analysis of Steepest Descent Method 7 Newtons Method and Convergence Analysis 8 Quasi Newton Methods-1 9 Quasi Newton Methods -2 10 Conjugate Gradient Method-1 11 Conjugate Gradient Method-2 12 Fundamentals of Constrained Optimization 13 Minimizing a differentiable function over a convex set 14 Karush-Kuhn-Tucker Conditions-1 15 Karush-Kuhn-Tucker Conditions-2 16 Active-Set Method 17 Quadratic Optimization-1 18 Quadratic Optimization-2 19 Quadratic Optimization-3 20 Penalty Function Method 21 Penalty Functions and Karush-Kuhn-Tucker Conditions 22 Sequential Quadratic Programming-1 23 Sequential Quadratic Programming-2 24 Conic Optimization 25 Semi-definite Programming-1 26 Semi-definite Programming-2 27 Lagrangian Relaxations for Integer Programming 28 SDP relaxations for quadratic integer programming 29 The S-Lemma and Quadratic Programming Duality-1 30 The S-Lemma and Quadratic Programming Duality-2 31 Duality in optimization 32 Duality in conic and semidefinite programming 33 Trust Region Methods-1 34 Trust Region Methods-2 35 Derivative Free Optimization-1 36 Derivative Free Optimization-2 37 Derivative Free Optimization-3 38 Derivatie Free Optimization-4 39 Derivative Free Optimization-5 40 Introduction to Calculus of Variations.

Calculus of several variables and linear algebra

Will be mentioned during the lectures.

Will be told during the lectures.