I was TA-ing my convex optimization class and explaining that [linear programs][1] are a special case of [second-order cone programs][2], which are themselves special cases of [semidefinite programs][3]. Is there any well-established class of optimization problems that is more general than semidefinite programs? *Conic optimization* problems would be an example of this, but I'm hoping for something a little more algebraic, if it exists.


  [1]: https://en.wikipedia.org/wiki/Linear_programming
  [2]: https://en.wikipedia.org/wiki/Second-order_cone_programming
  [3]: https://en.wikipedia.org/wiki/Semidefinite_programming