convex optimization

• for convex problems, local optima are global optima
• special cases
  • linear programming and all associated concepts
    • lagrange multipliers
    • interior point method
    • duality
• In linear programming, the objective is linear and the constraints are linear.
• In convex optimization, the objective is convex and the constraints are convex.
• See more here
• For lagrange multipliers, neither the objective or constraints have to be linear/convex. They can be anything as long as the gradients exist.