p-Lagrangian relaxation

p-Lagrangian relaxation is a novel technique to solve nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) with separable structures, such as those arising in deterministic equivalent representations of two-stage stochastic programming problems. In general, the nonconvex nature of these models still poses a challenge for available solvers, which do not consistently perform well for larger-scale instances. Therefore, we propose an appealing alternative algorithm that allows for overcoming computational performance issues. Our novel technique, named the p-Lagrangian relaxation, is a primal-dual decomposition method that combines a bundle-method inspired Lagrangian decomposition with mixed-integer programming-based relaxations. These relaxations are obtained using the reformulated normalised multiparametric disaggregation technique (RNMDT) and can be made arbitrarily precise by means of a precision parameter p. We provide a technical analysis showing the convergent behaviour of the approach as the approximation is made increasingly precise. We observe that, in addition to demonstrating superior performance in terms of convergence behaviour, the proposed method presents significant reductions in computational time.

Nikita Belyak
Nikita Belyak
Doctoral Candidate

Nikita Belyak is a Doctoral Candidate at the department of Mathematics and Systems Analysis of Aalto University.

Fabricio Oliveira
Fabricio Oliveira
Associate Professor of Operational Research

Fabricio Oliveira is an Associate Professor of Operational Research in the Department of Mathematics and Systems Analysis.

Related