The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Calculus of Variations

  • Morton I. Kamien
Reference work entry


The development of the calculus of variations is attributed to Euler and Lagrange, although some of it can be traced back to the Bernoullis. A history of the calculus of variations is provided by Goldstine (1980). The calculus of variations deals with the problem of determining a function that optimizes some criterion that is usually expressed as an integral. This problem is analogous to the differential calculus problem of finding a point at which a function is optimized, except that the point in the calculus of variations is a function rather than a number. The function over which the optimum is sought is usually restricted to the class of continuous and at least piecewise differentiable functions.

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Morton I. Kamien
    • 1
  1. 1.