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.[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][5]
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.[6]
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- ^ "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.
- ^ "Mathematical optimization". Engati. Retrieved 2024-08-24.
- ^ "Open Journal of Mathematical Optimization". ojmo.centre-mersenne.org. Retrieved 2024-08-24.