On generalized surrogate duality in mixed-integer nonlinear programming

Abstract The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global $$\epsilon $$ ϵ -optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due both theoretical practical considerations, relaxations of MINLPs are usually required be convex. Nonetheless, current optimization solvers can often successfully handle moderate presence nonconvexities, which opens the door use potentially tighter nonconvex relaxations. In this work, we exploit fact make relaxation obtained via aggregation constraints: surrogate These were actively studied linear integer in 70s 80s, but they have been scarcely considered since. We revisit these an MINLP setting show computational benefits challenges have. Additionally, study generalization such that allows multiple aggregations simultaneously present first algorithm capable computing best set aggregations. propose multitude enhancements improving its performance evaluate algorithm’s ability generate strong dual bounds through extensive experiments.