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
Stories about Maxima & Minima By V.M. Tikhomirov Pub: American Mathematical Society.
Convex Optimization By S. Boyd Pub: Cambridge University Press
Convex Analysis and Minimization Algorithms By J.B.Hiriat-Uruty& Lemarechal Pub: Springer
Convex Analysis By R.T.Rockafellar, Pub: Princeton
Stephen Byod lectures on Convex Optimization
Important: Please enable javascript in your browser and download Adobe Flash player to view this site
Site Maintained by Web Studio, IIT Madras. Contact Webmaster: nptel@iitm.ac.in