This paper explores a hitherto largely ignored dimension to norms in multi-agent systems: the normative role played by optimization objectives. We introduce the notion of optimization norms which constrain agent behaviour in a manner that is significantly distinct from norms in the traditional sense. We argue that optimization norms underpin most other norms, and offer a richer representation of these. We outline a methodology for identifying the optimization norms that underpin other norms. We then define a notion of compliance for optimization norms, as well as a notion of consistency and inconsistency resolution. We offer an algebraic formalization of valued optimization norms which allows us to explicitly reason about degrees of compliance and graded sanctions. We then outline an approach to decomposing and distributing sanctions amongst multiple agents in settings where there is joint responsibility.