Assignment 1

Select any two functions (for unconstrained optimisation) from the standard test functions from the libraries listed here and solve it using the standard functions available in the language of your choice. For example, in Matlab, you would use fmincon for constrained optimization and fminunc for unconstrained optimization. In Python, you would use scipy.optimize.minimize for both constrained and unconstrained optimization.

Report back the following:

1. Run the optimiser with multiple initial conditions and report the best solution found. (At least 5 initial conditions)

2. Report the number of iterations required to converge to the solution.

3. Now pick one initial condition and run the optimiser with three different choices of the algorithm. Report the best solution found and the number of iterations required to converge to the solution.

4. Now pick the best optimization algorithm and run the optimiser with three different choices of tolerance (For example, \(10^{-2}\), \(10^{-4}\), \(10^{-6}\)). Report the number of iterations required to converge to the solution.

5. Now set the optimiser to verbose mode and read through the output. List all the options available for the optimiser and understand what they do.

6. List the various stopping criteria available for the optimiser and think about how they make sense.

Deliverables

1. A report in PDF format with the above results and your observations.

2. A zip file containing the code used to generate the results.

Deadline 11:59 PM, 04/02/2024