Nonlinear Opt.: Basic concepts 2
In a non-linear problem there is either a non-linear objective function and no restrictions or a non-linear objective function and linear/non-linear restrictions or a linear objective function and non-linear restrictions.
Inhaltsverzeichnis
Theory
In opposite to the linear programming where we have the simplex algorithm to solve this there is not an universal algorithm to solve a non-linear problem.
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): restrictions(non-linear): g_i(x) \begin{Bmatrix} >= \\ = \\ <= \end{Bmatrix}~0 ~~~~~~~~~g_i(x) ~:= ~f_i(x) ~- ~b ~<= ~0 ~~~~~~(for~ i ~= ~1,...,n)
Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x_j~>=~0 ~~~~~~~~~~(for~j = 1,...,n)
Examples
Example 1 (non-linear objective function, no restrictions)
Example 2 (non-linear objective function, linear restrictions)
Example 3 (non-linear objective function, non-linear restrictions)
Example 4 (linear objective function, non-linear restrictions)
Sources
Internet sources
Literature
- Prof. Dr. Oliver Wendt: Operations Research Script, Summer Term 2013
- Immanuel M. Bomze/W. Grossmann: Optimierung - Theorie und Algorithmen, ISBN:3-411-1509-1
- Kurt Marti/Detlef Gröger: Einführung in die lineare und nichtlineare Optimierung, ISBN:3-790-81297-8
- Wolfgang Domschke/Andreas Drexl: Einführung in Operations Research 6. Auflage ISBN:3-540-23431-4
- Hans Corsten/Hilde Corsten/Carsten Sartor: Operations Research ISBN:9-783800-632022
