The simplex method (more precise "downhill simplex method") is to be understood
as a minimizing algorithm.
It can be used to optimize many kind of processes and products -
in the areas of CAD, economics, logistics, and many more.
A simplex is a geometric figure (an irregular volume) describing (containing)
the conditions of the problem to be solved (minimized).
The number of variables (n dimensions) of the problem to be solved corresponds
to the number of vertices (n+1) and to the number of planes (n-1) of the simplex
(i.e. a plane triangle for n = 2, a tetrahedron for n = 3).
The size of the simplex is continuously changed and mostly diminished,
so that it finally is small enough to contain the minimum with the desired accuracy:
the simplex is iteratively contracted and expanded.
The simplex method requires only function values, not derivatives,
which makes it easy to implement.