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Global optimization of non-convex generalized disjunctive programs: a review on reformulations and relaxation techniques

Author

Listed:
  • Juan P. Ruiz

    (Soteica Visual Mesa LLC)

  • Ignacio E. Grossmann

    (Carnegie Mellon University)

Abstract

In this paper we present a review on the latest advances in logic-based solution methods for the global optimization of non-convex generalized disjunctive programs. Considering that the performance of these methods relies on the quality of the relaxations that can be generated, our focus is on the discussion of a general framework to find strong relaxations. We identify two main sources of non-convexities that any methodology to find relaxations should account for. Namely, the one arising from the non-convex functions and the one arising from the disjunctive set. We review the work that has been done on these two fronts with special emphasis on the latter. We then describe different logic-based optimization techniques that make use of the relaxation framework and its impact through a set of numerical examples typically encountered in Process Systems Engineering. Finally, we outline challenges and future lines of work in this area.

Suggested Citation

  • Juan P. Ruiz & Ignacio E. Grossmann, 2017. "Global optimization of non-convex generalized disjunctive programs: a review on reformulations and relaxation techniques," Journal of Global Optimization, Springer, vol. 67(1), pages 43-58, January.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-016-0401-0
    DOI: 10.1007/s10898-016-0401-0
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    References listed on IDEAS

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    1. Ruiz, Juan P. & Grossmann, Ignacio E., 2012. "A hierarchy of relaxations for nonlinear convex generalized disjunctive programming," European Journal of Operational Research, Elsevier, vol. 218(1), pages 38-47.
    2. Faiz A. Al-Khayyal & James E. Falk, 1983. "Jointly Constrained Biconvex Programming," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 273-286, May.
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    Cited by:

    1. Yinrun Lyu & Li Chen & Changyou Zhang & Dacheng Qu & Nasro Min-Allah & Yongji Wang, 2018. "An interleaved depth-first search method for the linear optimization problem with disjunctive constraints," Journal of Global Optimization, Springer, vol. 70(4), pages 737-756, April.
    2. Harsha Nagarajan & Mowen Lu & Site Wang & Russell Bent & Kaarthik Sundar, 2019. "An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs," Journal of Global Optimization, Springer, vol. 74(4), pages 639-675, August.
    3. Jian, Jinbao & Pan, Shanshan & Yang, Linfeng, 2019. "Solution for short-term hydrothermal scheduling with a logarithmic size mixed-integer linear programming formulation," Energy, Elsevier, vol. 171(C), pages 770-784.
    4. Daniel Jornada & V. Jorge Leon, 2020. "Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 57-73, January.

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