Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives.^[1]^[2] It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering^[3] 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.

^ "The Nature of Mathematical Programming Archived 2014-03-05 at the Wayback Machine," Mathematical Programming Glossary, INFORMS Computing Society.
^ "Mathematical Programming: An Overview" (PDF). Retrieved 26 April 2024.
^ Martins, Joaquim R. R. A.; Ning, Andrew (2021-10-01). Engineering Design Optimization. Cambridge University Press. ISBN 978-1108833417.
^ 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.

[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.

[edo2021-3] 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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