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On convex relaxations of quadrilinear terms

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  • Sonia Cafieri
  • Jon Lee
  • Leo Liberti

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  • Sonia Cafieri & Jon Lee & Leo Liberti, 2010. "On convex relaxations of quadrilinear terms," Journal of Global Optimization, Springer, vol. 47(4), pages 661-685, August.
    • Handle: RePEc:spr:jglopt:v:47:y:2010:i:4:p:661-685
    DOI: 10.1007/s10898-009-9484-1
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    References listed on IDEAS

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    1. 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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    Citations

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    Cited by:

    1. Ruth Misener & Christodoulos Floudas, 2014. "ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations," Journal of Global Optimization, Springer, vol. 59(2), pages 503-526, July.
    2. Pete Janes & Alistair Rendell, 2013. "Deterministic global optimization in ab-initio quantum chemistry," Journal of Global Optimization, Springer, vol. 56(2), pages 537-558, June.
    3. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    4. Jean Lasserre & Tung Thanh, 2013. "Convex underestimators of polynomials," Journal of Global Optimization, Springer, vol. 56(1), pages 1-25, May.
    5. Alberto Del Pia & Aida Khajavirad, 2017. "A Polyhedral Study of Binary Polynomial Programs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 389-410, May.
    6. Peter Kirst & Oliver Stein & Paul Steuermann, 2015. "Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 591-616, July.
    7. Ruth Misener & Christodoulos A. Floudas, 2014. "A Framework for Globally Optimizing Mixed-Integer Signomial Programs," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 905-932, June.
    8. 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.
    9. 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.
    10. Emily Speakman & Jon Lee, 2018. "On branching-point selection for trilinear monomials in spatial branch-and-bound: the hull relaxation," Journal of Global Optimization, Springer, vol. 72(2), pages 129-153, October.
    11. Martin Ballerstein & Dennis Michaels, 2014. "Extended formulations for convex envelopes," Journal of Global Optimization, Springer, vol. 60(2), pages 217-238, October.
    12. Emily Speakman & Jon Lee, 2017. "Quantifying Double McCormick," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1230-1253, November.

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