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Optimization ○𓆪｜Definition｜1st｜20251119205401-00-⌔

Mathematical optimization - Wikipedia

Mathematical optimization

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Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.12 It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering3 to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.4

In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics.

Printed 2026-06-28.

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Footnotes

  1. “The Nature of Mathematical Programming Archived 2014-03-05 at the Wayback Machine,” Mathematical Programming Glossary, INFORMS Computing Society. ↩

  2. “Mathematical Programming: An Overview” (PDF). Retrieved 26 April 2024. ↩

  3. Martins, Joaquim R. R. A.; Ning, Andrew (2021-10-01). Engineering Design Optimization. Cambridge University Press. ISBN 978-1108833417. ↩

  4. Du, D. Z.; Pardalos, P. M.; Wu, W. (2008). “History of Optimization”. In Floudas, C.; Pardalos, P. (eds.). Encyclopedia of Optimization. Boston: Springer. pp. 1538–1542. ↩

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