"Matt J" wrote in message <email@example.com>... > > I'm not so sure. The function is not differentiable at the the boundary. The directional derivative goes to infinity when approached from the right and has no definition when approached from the left. This violates a lot of textbook assumptions. > > A solution might be to make the change of variables > > x_i=k_i*exp(z_i) > > leading to the reformulated problem
Hmmm. On second thought, that doesn't fix things, because if x_i wants to go to 0, then z_i will want to go to -Inf. You'll need to impose lower bounds on z_i, which is just the same as if you imposed x_i>=eps.