On Tue, Nov 23, 2010 at 11:37:02AM +0100, Sebastian Walter wrote: > >> min_x f(x) > >> s.t. lo <= Ax + b <= up > >> 0 = g(x) > >> 0 <= h(x)
> > No constraints. > didn't you say that you operate only in some convex hull? No. I have an initial guess that allows me to specify a convex hull in which the minimum should probably lie, but its not a constraint: nothing bad happens if I leave that convex hull. > > Either in R^n, in the set of integers (unidimensional), or in the set of > > positive integers. > According to http://openopt.org/Problems > this is a mixed integer nonlinear program http://openopt.org/MINLP . It is indead the name I know for it, however I have additional hypothesis (namely that f is roughly convex) which makes it much easier. > I don't have experience with the solver though, but it may take a long > time to run it since it uses branch-and-bound. Yes, this is too brutal: this is for non convex optimization. Dichotomy seems well-suited for finding an optimum on the set of intehers. > In my field of work we typically relax the integers to real numbers, > perform the optimization and then round to the next integer. > This is often sufficiently close a good solution. This is pretty much what I am doing, but you have to be careful: if the algorithm does jumps that are smaller than 1, it gets a zero difference between those jumps. If you are not careful, this might confuse a lot the algorithm and trick it into not converging. Thanks for your advice, Gaël _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
