Unformatted text preview: or the original problem. Solving this
problem multiple times, with diﬀerent c’s, will generate (perhaps diﬀerent) ǫ-suboptimal points. If
18 the problem has a strong minimum, these points will all be close to each other; if the problem has
a weak minimum, they can be quite diﬀerent.
There are diﬀerent strategies for choosing c in these experiments. The simplest is to choose the
c’s randomly; another method is to choose c to have the form ±ei , for i = 1, . . . , n. (This method
gives the ‘range’ of each component of x, over the ǫ-suboptimal set.)
You will carry out this method for the following problem, to determine whether it has a strong
minimum or a weak minimum. You can generate the vectors c randomly, with enough samples for
you to come to your conclusion. You can pick ǫ = 0.01p⋆ , which means that we are considering the
set of 1% suboptimal points.
The problem is a minimum fuel optimal control problem for a vehicle moving in R2 . The position
at time kh is g...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.
- Fall '13
- The Aeneid