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

 

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Untitled Document
 

Basic facts of maxima & minima & convex optimization.
Important classes of convex optimization problems.
Convex sets & convex functions
Differentiable convex functions
Projection on a convex set and normal cone
Sub differential of a convex.
Saddle point Conditions.
Karush-kuhn-Tucker Conditions
Lagrangian duality and examples.
Strong duality & consequences.
Linear programming, basics & examples.
Basic results and the fundamental theorems of linear programming
Simplex method
Introduction to interior point methods
Short step path following method .
Semi definite programming
Approximate solutions.

 

Lecture/Module

Topics

1

Basics of Convex Optimization

2

Basic facts of Convex Optimization

3

Basic properties of convex sets

4

Introduction to Polyhedral sets

5

Separation theorems for convex sets

6

Theorems of the alternative

7

Continuity and differentiability properties of convex functions

8

Non differentiable convex functions

9

Calculus of Sub differentials

10

Rockafeller-Pshenichny optimality condition

11

Properties of normals & projections

12

Computing the normal cone of inequality constraints.

13

Tangent cone

14

Fenchel conjugate continues.

15

Minimization of a convex function with convex inequality constraints is considered

16

Lagrangian Duality

17

Duality in connection with Linear Programming

18

Strong duality for convex problem

19

Pleasures of Linear Programming

20

Direction of descent

21

Extreme points of Linear Programming

22

Polyhedral sets & cones

23

Foundation of simplex methods

24

Fundamental theorem of Linear programming

25

Simplex methods

26

Simplex methods continued

27

Interior point methods

28

Interior point methods continued

29

Log barrier function

30

Primal-dual framework

31

Overview of interior point algorithm

32

Short step algorithm

33

Predictor-corrector method

34

Semi-definite programming

35

Saddle point type conditions for SDP.

36

Approximate solutions

37

Descent direction for non-smooth functions

38

Minimization of difference convex functions

39

Minimization of difference convex functions continues.

40

Concluding lecture.

Knowledge in Linear Algebra & Real Analysis


  1. Stories about Maxima & Minima By V.M. Tikhomirov Pub: American Mathematical Society.
  2. Convex Optimization By S. Boyd Pub: Cambridge University Press
  3. Convex Analysis and Minimization Algorithms By J.B.Hiriat-Uruty& Lemarechal Pub: Springer
  4. Convex Analysis By R.T.Rockafellar, Pub: Princeton

Stephen Byod lectures on Convex Optimization



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