Inexact solution of NLP subproblems in MINLP

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness in the limit case. Some numerical results will be presented to illustrate the behavior of the methods under NLP subproblem inexactness.