EAGO.jl: easy advanced global optimization in Julia

References

• B.M. Adams, W. Bohnhoff, K. Dalbey, J. Eddy, M. Eldred, D. Gay, K. Haskell, P.D. Hough, and L.P. Swiler, DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 5.0 user's manual, Tech. Rep. SAND2010-2183, Sandia National Laboratories, 2009.
   Google Scholar
• O. Andrzej and K. Stanislaw, Evolutionary algorithms for global optimization, in Global Optimization: Scientific and Engineering Case Studies, Chap. 12, Springer US, Boston, MA, 2006, pp. 267–300. Available at https://doi.org/10.1007/0-387-30927-6_12.
   Google Scholar
• M. Bartholomew-Biggs, S. Brown, B. Christianson, and L. Dixon, Automatic differentiation of algorithms, J. Comput. Appl. Math. 124 (2000), pp. 171–190. Available at https://doi.org/10.1016/S0377-0427(00)00422-2.
   Web of Science ®Google Scholar
• P.I. Barton and C. Pantelides, gPROMS – A combined discrete/continuous modelling environment for chemical processing systems, Simul. Ser. 25 (1993), pp. 25–25.
   Google Scholar
• P.I. Barton and C.C. Pantelides, Modeling of combined discrete/continuous processes, AIChE J. 40 (1994), pp. 966–979. Available at https://doi.org/10.1002/aic.690400608.
   Web of Science ®Google Scholar
• P. Belotti, CoUEnnE: A user's manual, Tech. Rep., Lehigh University, 2009.
   Google Scholar
• P. Belotti, J. Lee, L. Liberti, F. Margot, and A. Wächter, Branching and bounds tightening techniques for non-convex MINLP, Optim. Methods Softw. 24 (2009), pp. 597–634. doi: 10.1080/10556780903087124
   Web of Science ®Google Scholar
• L. Benet and D. Sanders, ValidatedNumerics.jl, 2019. Available at https://www.github.com/JuliaIntervals/ValidatedNumerics.jl.
   Google Scholar
• B.W. Bequette, Process Control: Modeling, Design, and Simulation, Prentice Hall Professional, Upper Saddle River, NJ, 2003.
   Google Scholar
• M. Berz and G. Hoffstätter, Computation and application of Taylor polynomials with interval remainder bounds, Reliab. Comput. 4 (1998), pp. 83–97. Available at https://doi.org/10.1023/A:1009958918582.
   Google Scholar
• J. Bezanson, A. Edelman, S. Karpinski, and V.B. Shah, Julia: A fresh approach to numerical computing, SIAM Rev. 59 (2017), pp. 65–98. doi: 10.1137/141000671
   Web of Science ®Google Scholar
• A. Bompadre and A. Mitsos, Convergence rate of McCormick relaxations, J. Global Optim. 52 (2012), pp. 1–28. Available at http://dx.doi.org/10.1007/s10898-011-9685-2.
   Web of Science ®Google Scholar
• D. Bongartz and A. Mitsos, Deterministic global optimization of process flowsheets in a reduced space using McCormick relaxations, J. Global Optim. 69 (2017), pp. 761–796. Available at https://doi.org/10.1007/s10898-017-0547-4.
   Web of Science ®Google Scholar
• D. Bongartz, J. Najman, S. Sass, and A. Mitsos, MAiNGO: McCormick based algorithm for mixed integer nonlinear global optimization, Tech. Rep., RWTH, Aachen, 2018.
   Google Scholar
• H. Cao, Y. Song, and K.A. Khan, Convergence of subtangent-based relaxations of nonlinear programs, Processes 7 (2019), p. 221. Available at https://doi.org/10.3390/pr7040221.
   Web of Science ®Google Scholar
• T. Coleman, M.A. Branch, and A. Grace, Optimization toolbox, For Use with MATLAB. User's Guide for MATLAB 5, Version 2, Release II, 1999.
   Google Scholar
• I.I. Cplex, IBM ILOG CPLEX optimizer, 2020. Available at http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/.
   Google Scholar
• L.H. De Figueiredo and J. Stolfi, Affine arithmetic: Concepts and applications, Numer. Algorithms 37 (2004), pp. 147–158. Available at https://doi.org/10.1023/B:NUMA.0000049462.70970.b6.
   Web of Science ®Google Scholar
• E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles, Math. Program. 91 (2002), pp. 201–213. Available at https://doi.org/10.1007/s101070100263.
   Web of Science ®Google Scholar
• F. Domes and A. Neumaier, Constraint propagation on quadratic constraints, Constraints 15 (2010), pp. 404–429. Available at https://doi.org/10.1007/s10601-009-9076-1.
   Web of Science ®Google Scholar
• I. Dunning, J. Huchette, and M. Lubin, JuMP: A modeling language for mathematical optimization, SIAM Rev. 59 (2017), pp. 295–320. Available at https://doi.org/10.1137/15M1020575.
   Web of Science ®Google Scholar
• C.A. Floudas and O. Stein, The adaptive convexification algorithm: A feasible point method for semi-infinite programming, SIAM J. Optim. 18 (2008), pp. 1187–1208. Available at http://dx.doi.org/10.1137/060657741.
   Web of Science ®Google Scholar
• R. Fourer, D.M. Gay, and B.W. Kernighan, A modeling language for mathematical programming, Manag. Sci. 36 (1990), pp. 519–554. Available at https://doi.org/10.1287/mnsc.36.5.519.
   Web of Science ®Google Scholar
• GAMS Development Corporation, GAMS – A User's Guide, GAMS Release 24.2.1, Washington, DC, USA, 2013. Available at http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf.
   Google Scholar
• A.M. Gleixner, T. Berthold, B. Müller, and S. Weltge, Three enhancements for optimization-based bound tightening, J. Global Optim. 67 (2017), pp. 731–757. Available at https://doi.org/10.1007/s10898-016-0450-4.
   Web of Science ®Google Scholar
• A. Griewank and A. Walther, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd ed., SIAM, Philadelphia, PA, 2008. Available at https://doi.org/10.1137/1.9780898717761.
   Google Scholar
• Gurobi Optimization, LLC, Gurobi optimizer reference manual, 2020. Available at http://www.gurobi.com.
   Google Scholar
• W.E. Hart, C.D. Laird, J.P. Watson, D.L. Woodruff, G.A. Hackebeil, B.L. Nicholson, and J.D. Siirola, Pyomo-Optimization Modeling in Python, 2nd ed., Vol. 67, Springer, Switzerland, 2012. Available at https://doi.org/10.1007/978-3-319-58821-6.
   Google Scholar
• R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, Springer, Berlin, 2013. Available at https://books.google.com/books?id=Pe_1CAAAQBAJ.
   Google Scholar
• IEEE, IEEE Standard for Interval Arithmetic, IEEE Std 1788-2015, 2015, pp. 1–97.
   Google Scholar
• R. Kannan and P.I. Barton, The cluster problem in constrained global optimization, J. Global Optim. 69 (2017), pp. 629–676. Available at https://doi.org/10.1007/s10898-017-0531-z.
   Web of Science ®Google Scholar
• A. Khajavirad and N.V. Sahinidis, A hybrid LP/NLP paradigm for global optimization relaxations, Math. Program. Comput. 10 (2018), pp. 383–421. Available at https://doi.org/10.1007/s12532-018-0138-5.
   Web of Science ®Google Scholar
• K.A. Khan, H.A.J. Watson, and P.I. Barton, Differentiable McCormick relaxations, J. Global Optim. 67 (2017), pp. 687–729. Available at http://dx.doi.org/10.1007/s10898-016-0440-6.
   Web of Science ®Google Scholar
• K.A. Khan, M. Wilhelm, M.D. Stuber, H. Cao, H.A.J. Watson, and P.I. Barton, Corrections to: differentiable McCormick relaxations, J. Global Optim. 70 (2018), pp. 705–706. Available at https://doi.org/10.1007/s10898-017-0601-2.
   Web of Science ®Google Scholar
• O. Kröger, C. Coffrin, H. Hijazi, and H. Nagarajan, Juniper: An open-source nonlinear branch-and-bound solver in Julia, in International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Springer, Cham, 2018, pp. 377–386.
   Google Scholar
• G.P. McCormick, Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems, Math. Program. 10 (1976), pp. 147–175. Available at http://dx.doi.org/10.1007/BF01580665.
   Web of Science ®Google Scholar
• R. Misener and C.A. Floudas, ANTIGONE: Algorithms for continuous/integer global optimization of nonlinear equations, J. Global Optim. 59 (2014), pp. 503–526. Available at https://doi.org/10.1007/s10898-014-0166-2.
   Web of Science ®Google Scholar
• A. Mitsos, Global optimization of semi-infinite programs via restriction of the right-hand side, Optimization 60 (2011), pp. 1291–1308. Available at http://dx.doi.org/10.1080/02331934.2010.527970.
   Web of Science ®Google Scholar
• A. Mitsos, B. Chachuat, and P.I. Barton, McCormick-based relaxations of algorithms, SIAM. J. Optim. 20 (2009), pp. 573–601. Available at https://doi.org/10.1137/080717341.
   Web of Science ®Google Scholar
• R. Moore, Methods and Applications of Interval Analysis, Studies in Applied and Numerical Mathematics, Society for Industrial and Applied Mathematics, SIAM, Philadelphia, PA, 1979. Available at https://books.google.com/books?id=bavU6VlOG4EC.
   Google Scholar
• R.E. Moore, Interval Analysis, Vol. 4, Prentice-Hall, Englewood Cliffs, NJ, 1966.
   Google Scholar
• J. Najman and A. Mitsos, Convergence analysis of multivariate McCormick relaxations, J. Global Optim. 66 (2016), pp. 1–32. Available at https://doi.org/10.1007/s10898-016-0408-6.
   Web of Science ®Google Scholar
• J. Najman and A. Mitsos, On tightness and anchoring of McCormick and other relaxations, J. Global Optim. (2017). Available at https://doi.org/10.1007/s10898-017-0598-6.
   Google Scholar
• J. Najman and A. Mitsos, Tighter McCormick relaxations through subgradient propagation, J. Global Optim. 75 (2019), pp. 565–593. Available at https://doi.org/10.1007/s10898-019-00791-0.
   Web of Science ®Google Scholar
• J. Najman, D. Bongartz, A. Tsoukalas, and A. Mitsos, Erratum to: Multivariate McCormick relaxations, J. Global Optim. 68 (2017), pp. 219–225. Available at https://doi.org/10.1007/s10898-016-0470-0.
   Web of Science ®Google Scholar
• A. Neumaier, Interval Methods for Systems of Equations, Vol. 37, Cambridge University Press, Cambridge, 1990.
   Google Scholar
• A. Neumaier, Second-order sufficient optimality conditions for local and global nonlinear programming, J. Global Optim. 9 (1996), pp. 141–151. Available at https://doi.org/10.1007/BF00121660.
   Web of Science ®Google Scholar
• A. Neumaier, O. Shcherbina, W. Huyer, and T. Vinkó, A comparison of complete global optimization solvers, Math. Program. 103 (2005), pp. 335–356. Available at https://doi.org/10.1007/s10107-005-0585-4.
   Web of Science ®Google Scholar
• Process Systems Enterprise, gPROMS. Available at http://www.psenterprise.com/products/gproms.
   Google Scholar
• Y. Puranik and N.V. Sahinidis, Domain reduction techniques for global NLP and MINLP optimization, Constraints 22 (2017), pp. 338–376. Available at https://doi.org/10.1007/s10601-016-9267-5.
   Web of Science ®Google Scholar
• T.K. Ralphs and L. Ladanyi, Symphony: A parallel framework for branch and cut, 1999. Available at https://www.coin-or.org/SYMPHONY/intro-2.7/symphony.html.
   Google Scholar
• J. Revels, Cassette.jl, 2018. Available at https://github.com/jrevels/Cassette.jl.
   Google Scholar
• J. Revels, M. Lubin, and T. Papamarkou, Forward-mode automatic differentiation in Julia, preprint (2016). Available at arXiv:1607.07892.
   Google Scholar
• H.S. Ryoo and N.V. Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Comput. Chem. Eng. 19 (1995), pp. 551–566. Available at https://doi.org/10.1016/0098-1354(94)00097-2.
   Web of Science ®Google Scholar
• N.V. Sahinidis, BARON: A general purpose global optimization software package, J. Global Optim. 8 (1996), pp. 201–205. Available at http://dx.doi.org/10.1007/BF00138693.
   Web of Science ®Google Scholar
• J.K. Scott, M.D. Stuber, and P.I. Barton, Generalized McCormick relaxations, J. Global Optim. 51 (2011), pp. 569–606. Available at https://doi.org/10.1007/s10898-011-9664-7.
   Web of Science ®Google Scholar
• X. Shen, S. Diamond, Y. Gu, and S. Boyd, Disciplined convex-concave programming, in Decision and Control (CDC), 2016 IEEE 55th Conference on, IEEE, 2016, pp. 1009–1014.
   Google Scholar
• A.B. Singer, Global dynamic optimization, Ph.D. diss., Massachusetts Institute of Technology, 2004. Available at http://hdl.handle.net/1721.1/28662.
   Google Scholar
• A.B. Singer, J.W. Taylor, P.I. Barton, and W.H. Green, Global dynamic optimization for parameter estimation in chemical kinetics, J. Phys. Chem. A 110 (2006), pp. 971–976. Available at https://doi.org/10.1021/jp0548873.
   PubMed Web of Science ®Google Scholar
• E.M. Smith and C.C. Pantelides, Global optimisation of nonconvex MINLPs, Comput. Chemical Eng. 21 (1997), pp. S791–S796. Available at http://dx.doi.org/10.1016/S0098-1354(97)87599-0. doi: 10.1016/S0098-1354(97)00146-4
   Web of Science ®Google Scholar
• M.D. Stuber, Evaluation of process systems operating envelopes, Ph.D. diss., Massachusetts Institute of Technology, 2013, Available at http://hdl.handle.net/1721.1/79143.
   Google Scholar
• M.D. Stuber, A differentiable model for optimizing hybridization of industrial process heat systems with concentrating solar thermal power, Processes 6 (2018), p. 76. Available at https://doi.org/10.3390/pr6070076.
   Web of Science ®Google Scholar
• M.D. Stuber and P.I. Barton, Semi-infinite optimization with implicit functions, Ind. Eng. Chem. Res. 54 (2015), pp. 307–317. Available at http://dx.doi.org/10.1021/ie5029123.
   Web of Science ®Google Scholar
• M.D. Stuber, J.K. Scott, and P.I. Barton, Convex and concave relaxations of implicit functions, Optim Methods Softw. 30 (2015), pp. 424–460. Available at https://doi.org/10.1080/10556788.2014.924514.
   Web of Science ®Google Scholar
• M.D. Stuber, A. Wechsung, A. Sundaramoorthy, and P.I. Barton, Worst-case design of subsea production facilities using semi-infinite programming, AIChE J. 60 (2014), pp. 2513–2524. Available at http://dx.doi.org/10.1002/aic.14447.
   Web of Science ®Google Scholar
• M. Tawarmalani and N. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Nonconvex Optimization and Its Applications, Springer, US, 2002. Available at https://books.google.com/books?id=MjueCVdGZfoC.
   Google Scholar
• M. Tawarmalani and N.V. Sahinidis, A polyhedral branch-and-cut approach to global optimization, Math. Program. 103 (2005), pp. 225–249. Available at http://dx.doi.org/10.1007/s10107-005-0581-8.
   Web of Science ®Google Scholar
• J.W. Taylor, G. Ehlker, H.H. Carstensen, L. Ruslen, R.W. Field, and W.H. Green, Direct measurement of the fast, reversible addition of oxygen to cyclohexadienyl radicals in nonpolar solvents, J. Phys. Chem. A 108 (2004), pp. 7193–7203. Available at https://doi.org/10.1021/jp0379547.
   Web of Science ®Google Scholar
• J.W. Tester and M. Modell, Thermodynamics and Its Applications, Prentice Hall PTR, Upper Saddle River, NJ, 1997.
   Google Scholar
• A. Tsoukalas and A. Mitsos, Multivariate McCormick relaxations, J. Global Optim. 59 (2014), pp. 633–662. Available at https://doi.org/10.1007/s10898-014-0176-0.
   Web of Science ®Google Scholar
• S. Vigerske, Decomposition in multistage stochastic programming and a constraint integer programming approach to mixed-integer nonlinear programming, Ph.D. diss., Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013.
   Google Scholar
• A. Wächter and L.T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program. 106 (2006), pp. 25–57. Available at https://doi.org/10.1007/s10107-004-0559-y.
   Web of Science ®Google Scholar
• A. Wechsung, J.K. Scott, H.A. Watson, and P.I. Barton, Reverse propagation of McCormick relaxations, J. Global Optim. 63 (2015), pp. 1–36. Available at https://doi.org/10.1007/s10898-015-0303-6.
   Web of Science ®Google Scholar
• M.E. Wilhelm, A.V. Le, and M.D. Stuber, Global optimization of stiff dynamical systems, AIChE J. 65 (2019), p. e16836. Available at https://doi.org/10.1002/aic.16836.
   Web of Science ®Google Scholar