Course abstract

• 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.