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Course Co-ordinated by IIT Kanpur
Coordinators
 
Dr. Joydeep Dutta
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.



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