convex functions

(6 hours to learn)


Intuitively, convex functions are bowl-shaped. They are significant in optimization, because it is often possible to efficiently find the global optimum of a convex function.


This concept has the prerequisites:


  • Know the definition of a convex function (in multiple dimensions)
  • Know and be able to apply alternative characterizations of convex functions
    • first-order condition (linear approximation lies below the function)
    • second-order condition (second derivative matrix is positive semidefinite)
  • Know some examples of convex functions
  • Why can the value of the function outside its domain be taken to be infinity?

Core resources (read/watch one of the following)


Convex Optimization
A graduate-level textbook on convex optimization.
Authors: Stephen Boyd,Lieven Vandenberghe
Other notes:
  • Some of the examples may use concepts you haven't seen. If so, just try to get the gist.

See also