Optimization (mathematics): Difference between revisions
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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'' | :''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''). | ||
Latest revision as of 21:28, 10 March 2008
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).
