It’s a very special case. Everything is affine so it’s equivalent of a linear program basically. A normal optimization problem, if every function is affine you have a linear program because you minimize and affine function, subject to affine functions less than zero because you’re conventionally called linear and inequalities. Affine equality, that’s just conventionally called linear equality constraints. So here, everything is affine. You minimize a linear function. Now this is a very, very interesting inequality. This is affine and this just says that FX + G is less than or equal to zero with respect to this cone. ...

See the whole transcript at Convex Optimization I - Lecture 07