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