0

I want to create a suite of test problems for a package of convex optimization methods I have implemented (gradient descent, conjugate gradient, BFGS, etc.).

I would ideally know the exact solution to the problem, and then check that these algorithms got a sufficiently close answer.

Currently, I'm doing maximum likelihood for a multivariate Gaussian (and using the above gradient-based methods rather than the closed-form answer).

What else do you recommend?

DBelanger
  • 411
  • 1
  • 4
  • 6
  • What is the question? Do you want examples of objective functions and their minimums, or some method to find the min. of your multivariate Gaussian? – AGS Aug 11 '12 at 00:23

1 Answers1

0

Find x to minimise ||A*x-b||. If b is A*y, and A is 1-1 the unique solution is y. If the norm is the usual one then this is just linear least squares, but the problem is convex for any norm. By choosing an A with large condition number you can make the problem difficult numerically.

dmuir
  • 614
  • 4
  • 4