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The p-Lagrangian relaxation for separable nonconvex MIQCQP problems

Author

Listed:
  • Tiago Andrade

    (PSR)

  • Nikita Belyak

    (Aalto University)

  • Andrew Eberhard

    (RMIT University)

  • Silvio Hamacher

    (Pontifical Catholic University of Rio de Janeiro)

  • Fabricio Oliveira

    (Aalto University)

Abstract

This paper presents a novel technique to compute Lagrangian bounds for nonconvex mixed-integer quadratically constrained quadratic programming problems presenting a separable structure (i.e., a separable problems) 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 to the 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 decomposition, is a decomposition method that combines Lagrangian decomposition with mixed-integer programming-based relaxations. These relaxations are obtained using the reformulated normalised multiparametric disaggregation technique 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 the proposed method presents significant reductions in computational time when compared with a previously proposed techniques in the literature and the direct employment of a commercial solver. Moreover, our computational experiments show that the employment of a simple heuristic can recover solutions with small duality gaps.

Suggested Citation

  • Tiago Andrade & Nikita Belyak & Andrew Eberhard & Silvio Hamacher & Fabricio Oliveira, 2022. "The p-Lagrangian relaxation for separable nonconvex MIQCQP problems," Journal of Global Optimization, Springer, vol. 84(1), pages 43-76, September.
  • Handle: RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01138-y
    DOI: 10.1007/s10898-022-01138-y
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    References listed on IDEAS

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    Cited by:

    1. Nikita Belyak & Steven A. Gabriel & Nikolay Khabarov & Fabricio Oliveira, 2023. "Renewable Energy Integration Strategies: A Transmission Operator's Perspective," Papers 2302.10562, arXiv.org, revised Mar 2024.

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