References¶
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- Bompadre, A. and Mitsos, A. (2012). Convergence rate of McCormick relaxations. Journal of Global Optimization, 52(1), 1–28. doi:10.1007/s10898-011-9685-2
- Frostig, R., Johnson, M. J. and Leary, C. (2018). Compiling machine learning programs via high-level tracing. SysML Conference. PDF
- Krawczyk, R. (1969). Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing, 4(3), 187–201. doi:10.1007/BF02234767
- Liberti, L. and Pantelides, C. C. (2003). Convex envelopes of monomials of odd degree. Journal of Global Optimization, 25(2), 157–168. doi:10.1023/A:1021924706467
- McCormick, G. P. (1976). Computability of global solutions to factorable nonconvex programs. Part I, convex underestimating problems. Mathematical Programming, 10, 147–175. doi:10.1007/BF01580665
- Mitsos, A., Chachuat, B. and Barton, P. I. (2009). McCormick-based relaxations of algorithms. SIAM Journal on Optimization, 20(2), 573–601. doi:10.1137/080717341
- Moore, R. E., Kearfott, R. B. and Cloud, M. J. (2009). Introduction to Interval Analysis. SIAM. doi:10.1137/1.9780898717716
- Najman, J. and Mitsos, A. (2019). Tighter McCormick relaxations through subgradient propagation. Journal of Global Optimization, 75(3), 565–593. doi:10.1007/s10898-019-00791-0
- Neumaier, A. (1990). Interval Methods for Systems of Equations. Cambridge University Press. doi:10.1017/CBO9780511526473
- Scott, J. K., Stuber, M. D. and Barton, P. I. (2011). Generalized McCormick relaxations. Journal of Global Optimization, 51(4), 569–606. doi:10.1007/s10898-011-9664-7
- Stuber, M. D., Scott, J. K. and Barton, P. I. (2015). Convex and concave relaxations of implicit functions. Optimization Methods and Software, 30(3), 424–460. doi:10.1080/10556788.2014.924514
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- Wilhelm, M. E. and Stuber, M. D. (2022). EAGO.jl: easy advanced global optimization in Julia. Optimization Methods and Software, 37(2), 425–450. doi:10.1080/10556788.2020.1786566
Software:
- JAX. Documentation
- pymcpp, the Python interface to MC++. PyPI
- EAGO. Documentation