Information Complexity of Mixed-Integer Convex Optimization

Amitabh Basu, Hongyi Jiang, Phillip A. Kerger, Marco Molinaro

Abstract: We investigate the information complexity of mixed-integer convex optimization under different kinds of oracles. We establish new lower bounds for the standard first-order oracle, improving upon the previous best known lower bound. This leaves only a lower order linear term (in the dimension) as the gap between the lower and upper bounds. Further, we prove the first set of results in the literature (to the best of our knowledge) on information complexity with respect to oracles based on first-order information but restricted to binary queries, and discuss various special cases of interest thereof.