Optimization (mathematics): Difference between revisions
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imported>Igor Grešovnik m (corrected: vectors in bold) |
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In [[mathematics]], the term '''optimization''' refers to study of problems in which one seeks for a minimum or a maximum of a real [[Function (mathematics)| function]] within a given allowed set. This problem can be presented in the following way: | In [[mathematics]], the term '''optimization''' refers to study of problems in which one seeks for a minimum or a maximum of a real [[Function (mathematics)| function]] within a given allowed set. This problem can be presented in the following way: | ||
:''Given:'' a [[function (mathematics)|function]] ''f'' : ''A'' <math>\to</math> '''R''' from some [[set]] ''A'' to the [[Real number|real numbers]] | :''Given:'' a [[function (mathematics)|function]] ''f'' : ''A'' <math>\to</math> '''R''' from some [[set]] ''A'' to the [[Real number|real numbers]] | ||
:''Find:'' an element '''x'''<sub>0</sub> in ''A'' such that ''f''('''x'''<sub>0</sub>) ≤ ''f''(''x'') for all ''x'' in ''A'' ("minimization") or such that ''f''(''x''<sub>0</sub>) ≥ ''f''('''x''') for all '''x''' | :''Find:'' an element '''x'''<sub>0</sub> in ''A'' such that ''f''('''x'''<sub>0</sub>) ≤ ''f''('''x''') for all '''x''' in ''A'' ("minimization") or such that ''f''('''x'''<sub>0</sub>) ≥ ''f''('''x''') for all '''x''' in ''A'' ("maximization"). | ||
Revision as of 09:37, 13 November 2007
In mathematics, the term optimization refers to study of problems in which one seeks for a minimum or a maximum of a real function within a given allowed set. This problem can be presented in the following way:
- Given: a function f : A R from some set A to the real numbers
- Find: an element x0 in A such that f(x0) ≤ f(x) for all x in A ("minimization") or such that f(x0) ≥ f(x) for all x in A ("maximization").
