Nonlinear programming

In mathematics, nonlinear programming (NLP) is the process of minimization or maximization of a function of a set of real variables (termed objective function), while simultaneously satisfying a set of equalities and inequalities ( collectively termed constraints), where some of the constraints or the objective function are nonlinear.

Mathematical formulation

A nonlinear programming problem can be stated as:

$\min _{{\mathbf {x}}\in X}f({\mathbf {x}})$

or

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

where

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

$X\subseteq R^{n}.$

In the above equations, the set X is also called the feasible region of the problem. The function to be minimized is often called the objective function or cost function.

See also

• Optimization

External links

• Nonlinear programming FAQ
• Mathematical Programming Glossary