References

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.

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.

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.

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).

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.