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Generalized McCormick relaxations

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  • Joseph Scott
  • Matthew Stuber
  • Paul Barton

Abstract

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Suggested Citation

  • Joseph Scott & Matthew Stuber & Paul Barton, 2011. "Generalized McCormick relaxations," Journal of Global Optimization, Springer, vol. 51(4), pages 569-606, December.
    • Handle: RePEc:spr:jglopt:v:51:y:2011:i:4:p:569-606
    DOI: 10.1007/s10898-011-9664-7
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    References listed on IDEAS

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    1. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    2. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    3. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    4. A. B. Singer & P. I. Barton, 2004. "Global Solution of Optimization Problems with Parameter-Embedded Linear Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 121(3), pages 613-646, June.
    5. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
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    Citations

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    Cited by:

    1. A. Skjäl & T. Westerlund & R. Misener & C. A. Floudas, 2012. "A Generalization of the Classical αBB Convex Underestimation via Diagonal and Nondiagonal Quadratic Terms," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 462-490, August.
    2. Jaromił Najman & Alexander Mitsos, 2019. "On tightness and anchoring of McCormick and other relaxations," Journal of Global Optimization, Springer, vol. 74(4), pages 677-703, August.
    3. Marco Locatelli, 2020. "Convex envelope of bivariate cubic functions over rectangular regions," Journal of Global Optimization, Springer, vol. 76(1), pages 1-24, January.
    4. Matthew E. Wilhelm & Matthew D. Stuber, 2023. "Improved Convex and Concave Relaxations of Composite Bilinear Forms," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 174-204, April.
    5. Artur M. Schweidtmann & Alexander Mitsos, 2019. "Deterministic Global Optimization with Artificial Neural Networks Embedded," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 925-948, March.
    6. Achim Wechsung & Paul Barton, 2014. "Global optimization of bounded factorable functions with discontinuities," Journal of Global Optimization, Springer, vol. 58(1), pages 1-30, January.
    7. Youssef M. Aboutaleb & Moshe Ben-Akiva & Patrick Jaillet, 2020. "Learning Structure in Nested Logit Models," Papers 2008.08048, arXiv.org.
    8. Jaromił Najman & Alexander Mitsos, 2016. "Convergence analysis of multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 66(4), pages 597-628, December.
    9. Jason Ye & Joseph K. Scott, 2023. "Extended McCormick relaxation rules for handling empty arguments representing infeasibility," Journal of Global Optimization, Springer, vol. 87(1), pages 57-95, September.
    10. Mario Villanueva & Boris Houska & Benoît Chachuat, 2015. "Unified framework for the propagation of continuous-time enclosures for parametric nonlinear ODEs," Journal of Global Optimization, Springer, vol. 62(3), pages 575-613, July.
    11. Joseph Scott & Paul Barton, 2013. "Improved relaxations for the parametric solutions of ODEs using differential inequalities," Journal of Global Optimization, Springer, vol. 57(1), pages 143-176, September.
    12. N. Kazazakis & C. S. Adjiman, 2018. "Arbitrarily tight $$\alpha $$ α BB underestimators of general non-linear functions over sub-optimal domains," Journal of Global Optimization, Springer, vol. 71(4), pages 815-844, August.
    13. Kamil A. Khan & Harry A. J. Watson & Paul I. Barton, 2017. "Differentiable McCormick relaxations," Journal of Global Optimization, Springer, vol. 67(4), pages 687-729, April.
    14. Jaromił Najman & Alexander Mitsos, 2019. "Tighter McCormick relaxations through subgradient propagation," Journal of Global Optimization, Springer, vol. 75(3), pages 565-593, November.
    15. Dominik Bongartz & Alexander Mitsos, 2017. "Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations," Journal of Global Optimization, Springer, vol. 69(4), pages 761-796, December.
    16. Spencer D. Schaber & Joseph K. Scott & Paul I. Barton, 2019. "Convergence-order analysis for differential-inequalities-based bounds and relaxations of the solutions of ODEs," Journal of Global Optimization, Springer, vol. 73(1), pages 113-151, January.
    17. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    18. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    19. Achim Wechsung & Spencer Schaber & Paul Barton, 2014. "The cluster problem revisited," Journal of Global Optimization, Springer, vol. 58(3), pages 429-438, March.
    20. Matthew E. Wilhelm & Chenyu Wang & Matthew D. Stuber, 2023. "Convex and concave envelopes of artificial neural network activation functions for deterministic global optimization," Journal of Global Optimization, Springer, vol. 85(3), pages 569-594, March.
    21. Achim Wechsung & Joseph Scott & Harry Watson & Paul Barton, 2015. "Reverse propagation of McCormick relaxations," Journal of Global Optimization, Springer, vol. 63(1), pages 1-36, September.
    22. Joseph K. Scott & Paul I. Barton, 2013. "Convex and Concave Relaxations for the Parametric Solutions of Semi-explicit Index-One Differential-Algebraic Equations," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 617-649, March.
    23. Huiyi Cao & Kamil A. Khan, 2023. "General convex relaxations of implicit functions and inverse functions," Journal of Global Optimization, Springer, vol. 86(3), pages 545-572, July.

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