The importance of designing proteins, such as high affinity antibodies, has become ever more apparent. Computational Protein Design can cast such design problems as optimization tasks with the objective of maximizing K*, an approximation of binding affinity. Here we lay out a graphical model framework for K* optimization that enables use of compact AND/OR search algorithms. We designed an AND/OR branch-and-bound algorithm, AOBB-K*, for optimizing K* that is guided by a new K* heuristic and can incorporate specialized performance improvements with theoretical guarantees. As AOBB-K* is inspired by algorithms from the well studied task of Marginal MAP, this work provides a foundation for harnessing advancements in state-of-the-art mixed inference schemes and adapting them to protein design.