w00t, another math guy around here.
Minimum Distance Using Lagrange Multipliers
Oh this stuff is pretty neat; I remember doing these optimization problems some time ago. As you might know, this topic gets really, really interesting when it is extended to funtionals in the calculus of variations; the Lagrange multiplier identity (
ÑF(v1,v2...) =
l Ñg1(v1,v2...) +
l Ñg2(v1,v2...)+ ... ) is just a special case of the generalized Euler-Lagrange equation for functionals (
¶f/
¶u -
¶/
¶v1 (
¶f/
¶(
¶u/
¶x ) ) = 0 ) when the independent function variables are constants. Some interesting problems in differential geometry and topology can be solved by applying an appropriate form of that equation: finding a geodesic given two points and a surface, finding minimal surfaces, finding the surface of minimal surface area and/or volume between two curves, etc. Really cool stuff.
