Convex optimization

The following sections are included:

• A geometric optimality criterion

• The Karush-Kuhn-Tucker conditions

• An example

• The Langrangian, saddle points, duality and game theory

• An interior point method

  • Newtonian descent, exact line search and bisection

  • Polyhedral constraints

• Maximizing convex functions over polytopes

  • Convex functions are continuous on open subsets

• Exercises