On Thursday, March 5, 2015 at 12:51:07 PM UTC-5, Iain Dunning wrote:
>
> I don't think anything in JuliaOpt other than NLOpt is going to play
> nicely with that non-convex L2 norm constraint.
>
Actually, I would tend to transform the problem to eliminate the equality
constraint:
min |Lx|_1 / |x|_2
and then turn the |Lx|_1 into a dummy variable t and add 2N inequality
constraints t >= (Lx)_i, t >= -(Lx)_i.
Nonlinear inequality constraints can be handled by NLopt, but in general I
find it is better to have a nonlinear objective than a nonlinear inequality
constraint when you have a choice, and in this particular problem that
isn't difficult. Then any algorithm that supports nonlinear objectives
and affine inequality constraints is applicable.
