Nonlinear programming: Difference between revisions
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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 [[Equation|equalities]] and [[inequality|inequalities]] ( collectively termed ''constraints''), where some of the constraints or the objective function are [[linearity|nonlinear]]. | 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 [[Equation|equalities]] and [[inequality|inequalities]] ( collectively termed ''constraints''), where some of the constraints or the objective function are [[linearity|nonlinear]]. | ||
== Mathematical formulation == | |||
A '''nonlinear programming problem''' can be stated as: | |||
:<math>\min_{x \in X}f(x)</math> | |||
or | |||
:<math>\max_{x \in X}f(x)</math> | |||
where | |||
:<math>f: R^n \to R</math> | |||
:<math>X \subseteq R^n.</math> | |||
Revision as of 12:30, 13 November 2007
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:
or
where
