(*F*, *c*) is an optimization problem, where *F* is the
set of feasible points and *c*(*f*) is a real-valued cost function.
The goal is to minimize *c* over *F*.

If *x* and *y* are real *n*-vectors, λ*x*
+ (1-λ)*y* is a convex combination of *x* and *y*
if 0 ≤ λ ≤ 1.

A set is convex if it is closed under convex combinations.

The intersection of any number of convex sets is convex.

A real-valued function c on a convex set S is convex if

c( λx+ (1-λ)y) ≤ λc(x) + (1-λ)c(y) for 0 ≤ λ ≤ 1.

If *c*(*x*) is a convex function on a convex set *S*,
then the set of points in *S* satisfying *c*(*x*) ≤
*t* is convex.