The p-Lagrangian relaxation for separable nonconvex MIQCQP problems

Abstract This paper presents a novel technique to compute Lagrangian bounds for nonconvex mixed-integer quadratically constrained quadratic programming problems presenting separable structure (i.e., problems) such as those arising in deterministic equivalent representations of two-stage stochastic problems. In general, the nature these models still poses challenge available solvers, which do not consistently perform well larger-scale instances. Therefore, we propose an appealing alternative algorithm that allows overcoming computational performance issues. Our technique, named p -Lagrangian decomposition, is decomposition method combines with programming-based relaxations. These relaxations are obtained using reformulated normalised multiparametric disaggregation and can be made arbitrarily precise by means precision parameter . We provide technical analysis showing convergent behaviour approach approximation increasingly precise. observe proposed significant reductions time when compared previously techniques literature direct employment commercial solver. Moreover, our experiments show simple heuristic recover solutions small duality gaps.