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''). | ||
Revision as of 11:17, 28 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).
See also
External links
- Mathematical Programming Glossary
- Mathematical optimization
- NEOS Guide currently being replaced by the NEOS Wiki - an extensive guide to optimization software
- Decision Tree for Optimization Software Links to optimization source codes
- Mathematical Programming Society
- COIN-OR - Computational Infrastructure for Operations Research
- Global optimization
- Optimization Related Links
- Optimization Online A repository for optimization e-prints
Optimization solvers
- CONOPT
- JOpt
- Mosek
- SAS OR
- Free Optimization Software by Systems Optimization Laboratory, Stanford University
- TANGO Project - Trustable Algorithms for Nonlinear General Optimization
Optimization libraries
- OOL (Open Optimization library) - a set of optimization routines in C.
- IOptLib (Investigative Optimization Library) - a free open source library for development of optimization algorithms (ANSI C).
- ALGLIB Optimization sources. C++, C#, Delphi, Visual Basic.