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Mixed integer nonlinear programming tools: an updated practical overview

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  • Claudia D’Ambrosio
  • Andrea Lodi

Abstract

We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties. Copyright Springer Science+Business Media New York 2013

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  • Claudia D’Ambrosio & Andrea Lodi, 2013. "Mixed integer nonlinear programming tools: an updated practical overview," Annals of Operations Research, Springer, vol. 204(1), pages 301-320, April.
    • Handle: RePEc:spr:annopr:v:204:y:2013:i:1:p:301-320:10.1007/s10479-012-1272-5
    DOI: 10.1007/s10479-012-1272-5
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    1. Ivo Nowak & Stefan Vigerske, 2008. "LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 127-138, June.
    2. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    3. R. C. Jeroslow, 1973. "There Cannot be any Algorithm for Integer Programming with Quadratic Constraints," Operations Research, INFORMS, vol. 21(1), pages 221-224, February.
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    2. Vicente Núñez-Antón & Juan Manuel Pérez-Salamero González & Marta Regúlez-Castillo & Carlos Vidal-Meliá, 2020. "Improving the Representativeness of a Simple Random Sample: An Optimization Model and Its Application to the Continuous Sample of Working Lives," Mathematics, MDPI, vol. 8(8), pages 1-27, July.
    3. Andreas Lundell & Jan Kronqvist, 2022. "Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT," Journal of Global Optimization, Springer, vol. 82(4), pages 863-896, April.
    4. Andrea Lodi & Giulia Zarpellon, 2017. "Rejoinder on: On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 247-248, July.
    5. Christoph Buchheim & Claudia D’Ambrosio, 2017. "Monomial-wise optimal separable underestimators for mixed-integer polynomial optimization," Journal of Global Optimization, Springer, vol. 67(4), pages 759-786, April.
    6. Kasina, Saamrat & Hobbs, Benjamin F., 2020. "The value of cooperation in interregional transmission planning: A noncooperative equilibrium model approach," European Journal of Operational Research, Elsevier, vol. 285(2), pages 740-752.
    7. Saeed Asadi Bagloee & Majid Sarvi & Avishai Ceder, 2017. "Transit priority lanes in the congested road networks," Public Transport, Springer, vol. 9(3), pages 571-599, October.
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    9. Mike G. Tsionas & Dionisis Philippas & Constantin Zopounidis, 2023. "Exploring Uncertainty, Sensitivity and Robust Solutions in Mathematical Programming Through Bayesian Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 205-227, June.
    10. 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.
    11. Adam N. Letchford & Qiang Ni & Zhaoyu Zhong, 2017. "An exact algorithm for a resource allocation problem in mobile wireless communications," Computational Optimization and Applications, Springer, vol. 68(2), pages 193-208, November.
    12. 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.

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