Used to find the Extremum of
subject to the constraint
,
where and are functions with continuous first Partial Derivatives on the Open
Set containing the curve
, and
at any point on the curve
(where is the Gradient). For an Extremum to exist,
(1) |
(2) |
(3) |
(4) |
(5) |
See also Kuhn-Tucker Theorem
References
Arfken, G. ``Lagrange Multipliers.'' §17.6 in Mathematical Methods for Physicists, 3rd ed.
Orlando, FL: Academic Press, pp. 945-950, 1985.