 Calculus of Variations and Optimal Control; Optimization  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to calculus of variations and optimization, which seek functions or geometric objects that optimize some objective function. This includes a discussion of techniques to find the optima, such as successive approximations or linear programming. In addition, there is quite a lot of work establishing the existence of optima and characterizing them. In many cases, optimal functions or curves can be expressed as solutions to differential equations. Common applications include seeking curves and surfaces that are minimal in some sense. However, the spaces on which the analyses are done may represent configurations of some physical system, say, so that this field also applies to optimization problems in economics or control theory for example. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
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