Nonlinear programming

Nonlinear programming (NLP) is the process of solving a system of equalities and inequalities over a set of unknown real variables, along with an objective function to be maximized. The problem can be stated simply as:

$\max _{x\in X}f(x)$

where

$f:R^{n}\to R$

$X\subseteq R^{n}$

If the objective function f is linear and the constrained space is a polytope, the problem is a linear programming problem.