Nonlinear Opt.: Basic concepts 3: Unterschied zwischen den Versionen

Version vom 28. Juni 2013, 11:57 Uhr

Theory

In contrast to the Linear Optimization, which solution method is the simplex algorithm, there is no comparable solution method für Nonlinear Optimization problems. Instead of the Simplex algorithm there are different solution methods which are specific for a given problem. But there is no gurantee for an optimal solution.

Theory

In contrast to the Linear Optimization, which solution method is the simplex algorithm, there is no comparable solution method für Nonlinear Optimization problems. Instead of the Simplex algorithm there are different solution methods which are specific for a given problem. But there is no gurantee for an optimal solution.

The gereral form of a non linear optimization can be stated as:

${\displaystyle max~z=f(x_{1},...,x_{n})}$

under the constraints that:

Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): h_{i}(x_{1},...,x_{n})\leq b_{i}\qquad i=1,...,m

and:

Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): x_{j}\geq 0\qquad j=1,...,n

Durch Umformen der Restriktion

Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): h_{i}(x_{1},...,x_{n})\leq b_{i}

in

Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): h_{i}(x_{1},...,x_{n})-b_{i}\leq 0

und der Benennung dieser Ungleichung mit g_{i} ${\displaystyle maxZ=f(x_{1},...,x_{n})}$