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Matlab zermelo m
AOE 5244
Optimization Techniques
HW Set 4
1. Consider the approximation to the Zermelo problem as implemented in
the file. We want to study the problem with a constraint
that (1) = . Modify the Matlab file to implement a penalty function
approach to this. Provide a brief description of your approach and numerical
results for a sequence of penalty parameter values. Consider the cases =
15 and = 3. Use values of the grid-parameter in the range 4 - 64,
depending on your computer resources. With the numerical results (you’ll need
to modify the code to provide some estimate for the gradient of the cost and
the constraint) check the optimality system.
2. Repeat Problem 1 with the augmented Lagrangian approach. Modify the
code to provide some estimate for the needed Lagrange multiplier.
3. Repeat Problem 1 with the constraint as an inequality (1) . Use
the Prob. 1 optimality results to test for optimality in the (now) inequality
constrained problem. Go through two-steps of either the augmented or (harder
?) projected Lagrangian method.
1
