Optimization is a numerical process of finding a solution to a problem by minimizing the returned value of an objective function. The objective function can be thought of as describing the cost or error in a particular solution. Optimization is used when a solution cannot be found through symbolic methods, usually to the complexity and non-linear nature of the problem.
The Nelder-Mead Method
The Nelder-Mead method uses the concept of a simplex, which is concept of a triangle in 2D space and a tetrahedron in 3D space generalized to N dimensions.