GitHub

References

Branch and Bound

  • 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.

Parametric Interval Techniques

  • 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.

Domain Reduction

  • 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.

Generalized McCormick Relaxations

  • 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.

Semi-Infinite Programming

  • 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.