How to do LQP with JOptimizer?

Question

I'm doing a thesis about the circles packing problem (CPP) in a circle, and I'm trying to learn how to use JOptimizer to do some simple optimization. Though my mathematical background is somewhat limited, and I'm having a hard time getting JOptimizer to work.

Taken from Packing circles in the smallest circle: an adaptive hybrid algorithm I have the following:

The CPP has a quite simple mathematical representation:

When converted to a 'semi-definite quadratically constrained linear programme' it becomes:

Now I'm a bit lost. How would I configure JOptimizer to optimize this (to a local minimum)? I also have a list of initial points and radii for my circles.

Thanks a lot!

Answer 1

The second sets of constraints of your problem are not a convex optimization domains, so you cannot use a convex optimization library to get a solution.