Question:
I am going to do a superquest project on least time paths given
certain restraints such as the path a race car would take to minimize its time
with its acceleration limited so that it does not skid. (or a robotic arm
moving some fragile object).

Replies:
The standard approach to "least time" problems like you mentioned
is known as known as "constrained optimization". I do not know a whole lot of
good references, but there are a lot of computational books on optimization.
This is also known as the "nonlinear programming" problem - sort of a silly
convention, but comes from the economics field, I think, where "linear
programming" has been dominant for a long time. There are actually a number
of packages already out there for doing these problems. You can find reviews
of some of them in the literature... I have used the IMSL "nconf" and "n0onf"
routines (the first just requires the function and constraints, the second
requires derivatives also). See if the machine you are running on has IMSL -
or look for other packages out there. I may have something you could use, if
you cannot find anything that works.

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