Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Least time paths
Name: hdog
Status: N/a
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993

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).

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.

Arthur Smith

Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory