The ellipsoid method

The ellipsoid is symmetry.

The relaxation of linear programing must be in it.

∴

Cj≧rj+pj, ∀j∈N (N={1,2,…,n}), ∀S⊆N

This is the whole universe, so you need to minimize it.

wj is weight.

You can also rewrite this.

This is the violation, so you remove the job k from S.