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Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation

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  • Mahdi Hamzeei
  • James Luedtke

Abstract

We present two linearization-based algorithms for mixed-integer nonlinear programs (MINLPs) having a convex continuous relaxation. The key feature of these algorithms is that, in contrast to most existing linearization-based algorithms for convex MINLPs, they do not require the continuous relaxation to be defined by convex nonlinear functions. For example, these algorithms can solve to global optimality MINLPs with constraints defined by quasiconvex functions. The first algorithm is a slightly modified version of the LP/NLP-based branch-and-bouund $$(\text{ LP/NLP-BB })$$ ( LP/NLP-BB ) algorithm of Quesada and Grossmann, and is closely related to an algorithm recently proposed by Bonami et al. (Math Program 119:331–352, 2009 ). The second algorithm is a hybrid between this algorithm and nonlinear programming based branch-and-bound. Computational experiments indicate that the modified LP/NLP-BB method has comparable performance to LP/NLP-BB on instances defined by convex functions. Thus, this algorithm has the potential to solve a wider class of MINLP instances without sacrificing performance. Copyright Springer Science+Business Media New York 2014

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  • Mahdi Hamzeei & James Luedtke, 2014. "Linearization-based algorithms for mixed-integer nonlinear programs with convex continuous relaxation," Journal of Global Optimization, Springer, vol. 59(2), pages 343-365, July.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:343-365
    DOI: 10.1007/s10898-014-0172-4
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    References listed on IDEAS

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    1. Kumar Abhishek & Sven Leyffer & Jeff Linderoth, 2010. "FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 555-567, November.
    2. Samir Elhedhli, 2006. "Service System Design with Immobile Servers, Stochastic Demand, and Congestion," Manufacturing & Service Operations Management, INFORMS, vol. 8(1), pages 92-97, December.
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    2. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Outer Approximation for Mixed-Integer Nonlinear Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1056-1086, December.

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