Merge pull request #3 from PSORLab/master

Update from master

Project.toml

@@ -31,8 +31,8 @@ IntervalArithmetic = "0.16.3, 0.16.4, 0.16.5, 0.16.6, 0.16.7"
 Ipopt = "0.6.0, 0.6.1"
 JuMP = "0.19.2, 0.20.0"
 MathOptInterface = "0.8.1, 0.8.2, 0.8.3, 0.8.4, ~0.9"
-McCormick = "0.4.2"
-ReverseMcCormick = "~0.4"
+McCormick = "0.5.1"
+ReverseMcCormick = "0.5.1"
 Reexport = "~0.2"
 NumericIO = "= 0.3.1"
 julia = "~1.2, ~1.3, ~1.4"

docs/src/ref.md

@@ -1,37 +1,37 @@
 # **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.
+- **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*
-- 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.
 
 ## *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.
 
 ## *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.
 
 ## *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.

src/EAGO.jl

@@ -15,6 +15,9 @@ module EAGO
     using DataStructures: BinaryMinMaxHeap, popmin!, popmax!, top
     using SparseArrays: SparseMatrixCSC, spzeros, rowvals, nzrange, nonzeros, sparse
     using LinearAlgebra: eigmin, norm
+
+    import IntervalArithmetic: mid
+
     @reexport using McCormick
     @reexport using ReverseMcCormick
 

src/eago_optimizer/optimizer.jl

@@ -185,7 +185,7 @@ Base.@kwdef mutable struct Optimizer <: MOI.AbstractOptimizer
     upper_factory::JuMP.OptimizerFactory = with_optimizer(Ipopt.Optimizer, print_level = 0)
     "Solve upper problem for every node with depth less than `upper_bounding_depth`
     and with a probabilityof (1/2)^(depth-upper_bounding_depth) otherwise (default = 4)"
-    upper_bounding_depth::Int64 = 4
+    upper_bounding_depth::Int64 = 6
 
     # Duality-based bound tightening (DBBT) options
     "Depth in B&B tree above which duality-based bound tightening should be disabled (default = 1E10)"