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# **References** | ||
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## *Branch and Bound* | ||
- Floudas, Christodoulos A. Deterministic global optimization: theory, methods and applications. Vol. 37. Springer Science & Business Media, 2013. | ||
- Horst, Reiner, and Hoang Tuy. Global optimization: Deterministic approaches. Springer Science & Business Media, 2013. | ||
- **Floudas, CA (2013)**. Deterministic global optimization: theory, methods and applications. Vol. 37. *Springer Science & Business Media*. | ||
- **Horst, R, Tuy, H (2013)**. Global optimization: Deterministic approaches. *Springer Science & Business Media*. | ||
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## *Parametric Interval Techniques* | ||
- E. R. Hansen and G. W. Walster. Global Optimization Using Interval Analysis. Marcel Dekker, New York, second edition, 2004. | ||
- R. Krawczyk. Newton-algorithmen zur bestimmung con nullstellen mit fehler-schranken. *Computing*, 4:187–201, 1969. | ||
- R. Krawczyk. Interval iterations for including a set of solutions. *Computing*, 32:13–31, 1984. | ||
- C. Miranda. Un’osservatione su un teorema di brower. *Boll. Un. Mat. Ital.*, 3:5–7, 1940. | ||
- A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge, 1990. | ||
- R. E. Moore. A test for existence of solutions to nonlinear systems. *SIAM Journal on Numerical Analysis*, 14(4):611–615, 1977. | ||
- **Hansen ER, Walster GW (2004)**. Global Optimization Using Interval Analysis. *Marcel Dekker, New York, second edition*. | ||
- **Krawczyk R (1969)**. Newton-algorithmen zur bestimmung con nullstellen mit fehler-schranken. *Computing*, 4:187–201. | ||
- **Krawczyk R (1984)**. Interval iterations for including a set of solutions. *Computing*, 32:13–31. | ||
- **Miranda C (1940)**. Un’osservatione su un teorema di brower. *Boll. Un. Mat. Ital.*, 3:5–7. | ||
- **Neumaier A (1990)**. Interval Methods for Systems of Equations. *Cambridge University Press*, Cambridge. | ||
- **Moore RE (1977)**. A test for existence of solutions to nonlinear systems. *SIAM Journal on Numerical Analysis*, 14(4):611–615. | ||
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## *Domain Reduction* | ||
- Benhamou, F., & Older, W.J. (1997). Applying interval arithmetic to real, integer, and boolean constraints. *The Journal of Logic Programming*, 32, 1–24. | ||
- Caprara, A., & Locatelli, M. (2010). Global optimization problems and domain reduction strategies. *Mathematical Programming*, 125, 123–137. | ||
- Gleixner, A.M., Berthold, T., Müller, B., & Weltge, S. (2016). Three enhancements for optimization-based bound tightening. ZIB Report, 15–16. | ||
- Ryoo, H.S., & Sahinidis, N.V. (1996). A branch-and-reduce approach to global optimization. *Journal of Global Optimization*, 8, 107–139. | ||
- Schichl, H., & Neumaier, A. (2005). Interval analysis on directed acyclic graphs for global optimization. *Journal of Global Optimization*, 33, 541–562. | ||
- Tawarmalani, M., & Sahinidis, N.V. (2005). A polyhedral branch-and-cut approach to global optimization. *Mathematical Programming*, 103, 225–249. | ||
- Vu, X., Schichl, H., & Sam-Haroud, D. (2009). Interval propagation and search on directed acyclic graphs for numerical constraint solving. *Journal of Global Optimization*, 45, 499–531. | ||
- **Benhamou F, & Older WJ (1997)**. Applying interval arithmetic to real, integer, and boolean constraints. *The Journal of Logic Programming*, 32, 1–24. | ||
- **Caprara A, & Locatelli M (2010)**. Global optimization problems and domain reduction strategies. *Mathematical Programming*, 125, 123–137. | ||
- **Gleixner AM, Berthold T, Müller B, & Weltge S (2016)**. Three enhancements for optimization-based bound tightening. *ZIB Report*, 15–16. | ||
- **Ryoo HS, & Sahinidis NV (1996)**. A branch-and-reduce approach to global optimization. *Journal of Global Optimization*, 8, 107–139. | ||
- **Schichl H, & Neumaier A (2005)**. Interval analysis on directed acyclic graphs for global optimization. *Journal of Global Optimization*, 33, 541–562. | ||
- **Tawarmalani, M, & Sahinidis, NV (2005)**. A polyhedral branch-and-cut approach to global optimization. *Mathematical Programming*, 103, 225–249. | ||
- **Vu, X, Schichl, H, & Sam-Haroud, D (2009)**. Interval propagation and search on directed acyclic graphs for numerical constraint solving. *Journal of Global Optimization*, 45, 499–531. | ||
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## *Generalized McCormick Relaxations* | ||
- Chachuat, B.: MC++: a toolkit for bounding factorable functions, v1.0. Retrieved 2 July 2014 https://projects.coin-or.org/MCpp (2014) | ||
- A. Mitsos, B. Chachuat, and P. I. Barton. McCormick-based relaxations of algorithms. *SIAM Journal on Optimization*, 20(2):573–601, 2009. | ||
- G. P. McCormick. Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems. *Mathematical Programming*, 10:147–175, 1976. | ||
- G. P. McCormick. Nonlinear programming: Theory, Algorithms, and Applications. Wiley, New York, 1983. | ||
- J. K. Scott, M. D. Stuber, and P. I. Barton. Generalized McCormick relaxations. *Journal of Global Optimization*, 51(4):569–606, 2011. | ||
- Stuber, M.D., Scott, J.K., Barton, P.I.: Convex and concave relaxations of implicit functions. *Optim. Methods Softw.* 30(3), 424–460 (2015) | ||
- A. Tsoukalas and A. Mitsos. Multivariate McCormick Relaxations. *Journal of Global Optimization*, 59:633–662, 2014. | ||
- K.A. Khan, HAJ Watson, P.I. Barton. Differentiable McCormick relaxations. *Journal of Global Optimization*, 67(4):687-729 (2017). | ||
- A., Wechsung JK Scott, HAJ Watson, and PI Barton. Reverse propagation of McCormick relaxations. *Journal of Global Optimization* 63(1):1-36 (2015). | ||
- **Chachuat, B (2014).** MC++: a toolkit for bounding factorable functions, v1.0. Retrieved 2 July 2014 https://projects.coin-or.org/MCpp | ||
- **Mitsos A, Chachuat B, and Barton PI. (2009).** McCormick-based relaxations of algorithms. *SIAM Journal on Optimization*, 20(2):573–601. | ||
- **McCormick, GP (1976).**. Computability of global solutions to factorable nonconvex programs: Part I-Convex underestimating problems. *Mathematical Programming*, 10:147–175. | ||
- **McCormick, GP (1983)**. Nonlinear programming: Theory, Algorithms, and Applications. Wiley, New York. | ||
- **Scott JK, Stuber MD, and Barton PI. (2011).** Generalized McCormick relaxations. *Journal of Global Optimization*, 51(4):569–606. | ||
- **Stuber MD, Scott JK, Barton PI (2015).** Convex and concave relaxations of implicit functions. *Optim. Methods Softw.* 30(3), 424–460 | ||
- **Tsoukalas A and Mitsos A (2014).** Multivariate McCormick Relaxations. *Journal of Global Optimization*, 59:633–662. | ||
- **Khan KA, Watson HAJ, Barton PI (2017).** Differentiable McCormick relaxations. *Journal of Global Optimization*, 67(4):687-729. | ||
- **Wechsung A, Scott JK, Watson HAJ, and Barton PI. (2015).** Reverse propagation of McCormick relaxations. *Journal of Global Optimization* 63(1):1-36. | ||
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## *Semi-Infinite Programming* | ||
- A. Mitsos. Global optimization of semi-infinite programs via restriction of the right-hand side. *Optimization*, 60(10-11):1291-1308, 2009. | ||
- Stuber, M.D. and Barton, P. I. Semi-Infinite Optimization With Implicit Functions. *Industrial & Engineering Chemistry Research*, 54:307-317, 2015. | ||
- **Mitsos A (2009).** Global optimization of semi-infinite programs via restriction of the right-hand side. *Optimization*, 60(10-11):1291-1308. | ||
- **Stuber MD and Barton PI (2015).** Semi-Infinite Optimization With Implicit Functions. *Industrial & Engineering Chemistry Research*, 54:307-317, 2015. |
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