T. Achterberg, T. Koch, and A. Martin. Branching rules revisited. Operations Research Letters, 33(1):42–54, 2005.

T. Achterberg. Constraint Integer Programming. PhD thesis, Technische Universität Berlin, 2007.

T. Achterberg. SCIP: Solving Constraint Integer Programs. Mathematical Programming Computations, 1(1):1–41, 2009.

C. S. Adjiman, I. P. Androulakis, and C. A. Floudas. A global optimization method, αBB, for general twice differentiable NLPs – II. Implementation and computational results. Computers & Chemical Engineering, 22(9):1159–1179, 1998.

C. S. Adjiman, S. Dallwig, C. A. Floudas, and A. Neumaier. A global optimization method, αBB, for general twice differentiable NLPs – I. Theoretical advances. Computers & Chemical Engineering, 22(9):1137–1158, 1998.

S. Ahmed, M. Tawarmalani, and N. V. Sahinidis. A finite branch-and-bound algorithm for two-stage stochastic integer programs. Mathematical Programming, 100(2):355–377, 2004.

P. R. Amestoy, I. S. Duff, J. Koster, and J.-Y. L'Excellent. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal of Matrix Analysis and Applications, 23(1):15–24, 2001.

P. R. Amestoy, A. Guermouche, J.-Y. L'Excellent, and S. Pralet. Hybrid scheduling for the parallel solution of linear systems. Parallel Computing, 32(2):136–156, 2006.

I. P. Androulakis, C. D. Maranas, and C. A. Floudas. αBB: A global optimization method for general constrained nonconvex problems. Journal of Global Optimization, 7(4):337–363, 1995.

C. Audet, P. Hansen, B. Jaumard, and G. Savard. A branch and cut algorithm for nonconvex quadratically constrained quadratic programming. Mathematical Programming, 87(1):131–152, 2000.

X. Bao, N. V. Sahinidis, and M. Tawarmalani. Multiterm polyhedral relaxations for nonconvex, quadratically-constrained quadratic programs. Optimization Methods and Software, 24(4-5):485–504, 2009.

X. Bao, N. V. Sahinidis, and M. Tawarmalani. Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons. Mathematical Programming, 129(1):129–157, 2011.

X. Bao, A. Khajavirad, N. V. Sahinidis, and M. Tawarmalani. Global optimization of nonconvex problems with multilinear intermediates. Mathematical Programming Computation, 7(1):1–37, 2015.

J. F. Bard. Practical bilevel optimization: Algorithms and applications, volume 30 of Nonconvex optimization and its applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.

R. H. Bartels and G. H. Golub. The simplex method of linear programming using the LU decomposition. Communications of the ACM, 12(5):266–268, 1969.

R. H. Bartels. A stabilization of the simplex method. Numerische Mathematik, 16(5):414–434, 1971.

P. Belotti, J. Lee, L. Liberti, F. Margot, and A. Wächter. Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods and Software, 24(4–5):597–634, 2009.

D. E. Bernal, S. Vigerske, F. Trespalacios, and I. E. Grossmann. Improving the performance of DICOPT in convex MINLP problems using a feasibility pump, 2017.

Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, Leona Gottwald, Christoph Graczyk, Katrin Halbig, Alexander Hoen, Christopher Hojny, Rolf van der Hulst, Thorsten Koch, Marco Lübbecke, Stephen J. Maher, Frederic Matter, Erik Mühmer, Benjamin Müller, Marc E. Pfetsch, Daniel Rehfeldt, Steffan Schlein, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Boro Sofranac, Mark Turner, Stefan Vigerske, Fabian Wegscheider, Philipp Wellner, Dieter Weninger, and Jakob Witzig. The SCIP Optimization Suite 8.0. ZIB Report 21-41, Zuse Institute Berlin, 2021.

Ksenia Bestuzheva, Antonia Chmiela, Benjamin Müller, Felipe Serrano, Stefan Vigerske, and Fabian Wegscheider. Global optimization of mixed-integer nonlinear programs with SCIP 8. Journal of Global Optimization, 2023.

L. T. Biegler. Nonlinear Programming: Concepts, Algorithms and Applications to Chemical Processes. MOS-SIAM Series on Optimization. SIAM, Philadelphia, 2010.

S. C. Billups and M. C. Ferris. QPCOMP: A quadratic program based solver for mixed complementarity problems. Mathematical Programming, 76(3):533–562, 1997.

S. C. Billups. Algorithms for Complementarity Problems and Generalized Equations. PhD thesis, University of Wisconsin–Madison, Madison, Wisconsin, 1995.

S. C. Billups. Improving the robustness of descent-based methods for semismooth equations using proximal perturbations. Mathematical Programming, 87(1):153–175, 2000.

Suresh Bolusani, Mathieu Besançon, Ksenia Bestuzheva, Antonia Chmiela, João Dionísio, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Mohammed Ghannam, Ambros Gleixner, Christoph Graczyk, Katrin Halbig, Ivo Hedtke, Alexander Hoen, Christopher Hojny, Rolf van der Hulst, Dominik Kamp, Thorsten Koch, Kevin Kofler, Jurgen Lentz, Julian Manns, Gioni Mexi, Erik Mühmer, Marc E. Pfetsch, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Mark Turner, Stefan Vigerske, Dieter Weninger, and Lixing Xu. The SCIP Optimization Suite 9.0. arXiv 2402.17702, 2024.

A. Bompadre and A. Mitsos. Convergence rate of McCormick relaxations. Journal of Global Optimization, 52(1):1–28, 2011.

P. Bonami, G. Cornuéjols, A. Lodi, and F. Margot. A feasibility pump for mixed integer nonlinear programs. Mathematical Programming, 119(2):331–352, 2009.

J. Bracken and J. T. McGill. Mathematical programs with optimization problems in the constraints. Operations Research, 21(1):37–44, 1973.

R. H. Byrd, M. E. Hribar, and J. Nocedal. An interior point algorithm for large scale nonlinear programming. SIAM Journal on Optimization, 9(4):877–900, 1999.

R. H. Byrd, J. C. Gilbert, and J. Nocedal. A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89(1):149–185, 2000.

R. H. Byrd, J. Nocedal, and R. A. Waltz. Feasible interior methods using slacks for nonlinear optimization. Computational Optimization and Applications, 26(1):35–61, 2003.

R. H. Byrd, N. I. M. Gould, J. Nocedal, and R. A. Waltz. An algorithm for nonlinear optimization using linear programming and equality constrained subproblems. Mathematical Programming, Series B, 100(1):27–48, 2004.

R. H. Byrd, N. I. M. Gould, J. Nocedal, and R. A. Waltz. On the convergence of successive linear-quadratic programming algorithms. SIAM Journal on Optimization, 16(2):471–489, 2005.

R. M. Chamberlain, M. J. D. Powell, and C. Lemaréchal. The watchdog technique for forcing convergence in algorithms for constrained optimization, volume 16 of Mathematical Programming Studies, pages 1–17. Springer, Berlin, Heidelberg, 1982.

Y. Chang and N. V. Sahinidis. Global optimization in stabilizing controller design. Journal of Global Optimization, 38(4):509–526, 2007.

V. Chvátal. Linear Programming. W. H. Freeman and Compan, New York, 1983.

A. R. Conn. Constrained optimization using a nondifferentiable penalty function. SIAM Journal on Numerical Analysis, 10(4):760–784, 1973.

R. W. Cottle and G. B. Dantzig. Complementary pivot theory of mathematical programming. Linear Algebra and its Applications, 1(1):103–125, 1968.

R. W. Cottle, J. S. Pang, and R. E. Stone. The Linear Complementarity Problem. Academic Press, Boston, 1992.

G. B. Dantzig. Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.

S. Devarajan, J. D. Lewis, and S. Robinson. Policy lessons from trade-focused, two-sector models. Journal of Policy Modeling, 12(4):625–657, 1990.

Paul Dierckx. Curve and Surface Fitting with Splines. Oxford University Press, 1993.

S. P. Dirkse and M. C. Ferris. MCPLIB: a collection of nonlinear mixed complementarity problems. Optimization Methods and Software, 5(4):319–345, 1995.

S. P. Dirkse and M. C. Ferris. A path search damped Newton method for computing general equilibria. Annals of Operations Research, 68(2):211–232, 1996.

S. P. Dirkse and M. C. Ferris. Crash techniques for large-scale complementarity problems. In M. C. Ferris and J. S. Pang, editors, Complementarity and Variational Problems: State of the Art, pages 40–61. SIAM Publications, 1997.

S. P. Dirkse and M. C. Ferris. Traffic modeling and variational inequalities using GAMS. In K. Tanczos Ph. L. Toint, M. Labbe and G. Laporte, editors, Operations Research and Decision Aid Methodologies in Traffic and Transportation Management, volume 166, pages 136–163. NATO ASI Series F, Philadelphia, Pennsylvania, 1998.

S. P. Dirkse. Robust Solution of Mixed Complementarity Problems. PhD thesis, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 1994.

F. Domes and A. Neumaier. Constraint propagation on quadratic constraints. Constraints, 15(3):404–429, 2010.

F. Domes and A. Neumaier. Rigorous enclosures of ellipsoids and directed cholesky factorizations. SIAM Journal on Matrix Analysis and Applications, 32(1):262–285, 2011.

M. C. Dorneich and N. V. Sahinidis. Global optimization algorithms for chip layout and compaction. Engineering Optimization, 25(2):131–154, 1995.

Marco A. Duran and Ignacio E. Grossmann. A mixed-integer nonlinear programming algorithm for process systems synthesis. AIChE Journal, 32(4):592–606, 1986.

Marco A. Duran and Ignacio E. Grossmann. An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming, 36(3):307–339, 1986.

S. K. Eldersveld. Large-scale sequential quadratic programming algorithms. PhD thesis, Department of Operations Research, Stanford University, Stanford, CA, 1991.

R. Ericson and A. Pakes. Markov perfect industry dynamics: A framework for empirical analysis. The Review of Economic Studies, 62(1):53–82, 1995.

M. C. Ferris and S. Lucidi. Nonmonotone stabilization methods for nonlinear equations. Journal of Optimization Theory and Applications, 81(1):53–71, 1994.

M. C. Ferris and T. S. Munson. Interfaces to PATH 3.0: Design, implementation and usage. Computational Optimization and Applications, 12(1-3):207–227, 1999.

M. C. Ferris and T. S. Munson. Preprocessing complementarity problems. In Michael C. Ferris, Olvi L. Mangasarian, and Jong-Shi Pang, editors, Complementarity: Applications, Algorithms and Extensions, pages 143–164. Springer US, Boston, MA, 2001.

M. C. Ferris and J. S. Pang, editors. Complementarity and Variational Problems: State of the Art. SIAM Publications, Philadelphia, Pennsylvania, 1997.

M. C. Ferris and J. S. Pang. Engineering and economic applications of complementarity problems. SIAM Review, 39(4):669–713, 1997.

M. C. Ferris, C. Kanzow, and T. S. Munson. Feasible descent algorithms for mixed complementarity problems. Mathematical Programming, 86(3):475–497, 1999.

M. C. Ferris, A. Meeraus, and T. F. Rutherford. Computing Wardropian equilibria in a complementarity framework. Optimization Methods and Software, 10(5):669–685, 1999.

A. Fischer. A special Newton–type optimization method. Optimization, 24(3-4):269–284, 1992.

R. Fletcher. An ell ₁ penalty method for nonlinear constraints. In P. T. Boggs, R. H. Byrd, and R. B. Schnabel, editors, Numerical Optimization 1984, pages 26–40, Philadelphia, 1985. SIAM.

C. A. Floudas and C. E. Gounaris. A review of recent advances in global optimization. Journal of Global Optimization, 45(1):3–38, 2009.

C. A. Floudas, I. G. Akrotirianakis, S. Caratzoulas, C. A. Meyer, and J. Kallrath. Global optimization in the 21st century: Advances and challenges. Computers & Chemical Engineering, 29(6):1185–1202, 2005.

C. A. Floudas. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, New York, NY, 1995.

C. A. Floudas. Deterministic Global Optimization: Theory, Algorithms and Applications, volume 37 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, Dordrecht, Netherlands, 2000.

Robert Fourer, Jun Ma, and Kipp Martin. OSiL: An instance language for optimization. Computational Optimization and Applications, 45(1):181–203, 2010.

R. Fourer. Solving staircase linear programs by the simplex method – 1: Inversion. Mathematical Programming, 23(1):274–313, 1982.

J. Fourtany-Amat and B. McCarl. A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society, 32(9):783–792, 1981.

K. Furman and I. P. Androulakis. A novel MINLP-based representation of the original complex model for predicting gasoline emissions. Computers & Chemical Engineering, 32(12):2857–2876, 2008.

K. Furman, N. Sawaya, and I. E. Grossmann. A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function. E-Print 5544, Optimization Online, 2016.

Gerald Gamrath, Tobias Fischer, Tristan Gally, Ambros M. Gleixner, Gregor Hendel, Thorsten Koch, Stephen J. Maher, Matthias Miltenberger, Benjamin Müller, Marc E. Pfetsch, Christian Puchert, Daniel Rehfeldt, Sebastian Schenker, Robert Schwarz, Felipe Serrano, Yuji Shinano, Stefan Vigerske, Dieter Weninger, Michael Winkler, Jonas T. Witt, and Jakob Witzig. The SCIP Optimization Suite 3.2. ZIB Report 15-60, Zuse Institute Berlin, 2016.

Gerald Gamrath, Daniel Anderson, Ksenia Bestuzheva, Wei-Kun Chen, Leon Eifler, Maxime Gasse, Patrick Gemander, Ambros Gleixner, Leona Gottwald, Katrin Halbig, Gregor Hendel, Christopher Hojny, Thorsten Koch, Pierre Le Bodic, Stephen J. Maher, Frederic Matter, Matthias Miltenberger, Erik Mühmer, Benjamin Müller, Marc Pfetsch, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Christine Tawfik, Stefan Vigerske, Fabian Wegscheider, Dieter Weninger, and Jakob Witzig. The SCIP Optimization Suite 7.0. ZIB Report 20-10, Zuse Institute Berlin, 2020.

E. P. Gatzke, J. E. Tolsma, and P. I. Barton. Construction of convex relaxations using automated code generation techniques. Optimization and Engineering, 3(3):305–326, 2002.

A. M. Geoffrion. Elements of Large-Scale Mathematical Programming – I. Concepts. Management Science, 16(11):652–675, 1970.

V. Ghildyal and N. V. Sahinidis. Solving global optimization problems with BARON. In A. Migdalas, P. M. Pardalos, and P. Värbrand, editors, From Local to Global Optimization, volume 53 of Nonconvex Optimization and Its Applications, chapter 10, pages 205–230. Springer, 2001.

V. Ghildyal. Design and development of a global optimization system. Master's thesis, Department of Mechanical & Industrial Engineering, University of Illinois, Urbana, IL, 1997.

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. Two step-length algorithms for numerical optimization. Technical Report SOL 79–25, Department of Operations Research, Stanford University, Stanford, California, 1979.

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. User's guide for NPSOL (Version 4.0): a Fortran package for nonlinear programming. Technical Report SOL 86–2, Department of Operations Research, Stanford University, Stanford, CA, 1986.

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. Maintaining LU factors of a general sparse matrix. Linear Algebra and its Applications, 88-89:239–270, 1987.

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. A practical anti-cycling procedure for linearly constrained optimization. Mathematical Programming, 45(1-3):437–474, 1989.

P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. Some theoretical properties of an augmented Lagrangian merit function. In P. M. Pardalos, editor, Advances in Optimization and Parallel Computing, pages 101–128. Elsevier Science Inc, 1992.

P. E. Gill, W. Murray, and M. A. Saunders. SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM Journal on Optimization, 12(4):979–1006, 2002.

P. E. Gill, W. Murray, and M. A. Saunders. SNOPT: An SQP algorithm for large-scale constrained optimization. SIAM Review, 47(1):99–131, 2005.

P. E. Gill, W. Murray, and M. A. Saunders. User's guide for SQOPT version 7: Software for large-scale linear and quadratic programming. Numerical analysis report, Department of Mathematics, University of California, San Diego, La Jolla, CA, 2006.

Ambros Gleixner, Leon Eifler, Tristan Gally, Gerald Gamrath, Patrick Gemander, Robert Lion Gottwald, Gregor Hendel, Christopher Hojny, Thorsten Koch, Matthias Miltenberger, Benjamin Müller, Marc E. Pfetsch, Christian Puchert, Daniel Rehfeldt, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Jan Merlin Viernickel, Stefan Vigerske, Dieter Weninger, Jonas T. Witt, and Jakob Witzig. The SCIP Optimization Suite 5.0. ZIB Report 17-61, Zuse Institute Berlin, 2017.

Ambros Gleixner, Michael Bastubbe, Leon Eifler, Tristan Gally, Gerald Gamrath, Robert Lion Gottwald, Gregor Hendel, Christopher Hojny, Thorsten Koch, Marco E. Lübbecke, Stephen J. Maher, Matthias Miltenberger, Benjamin Müller, Marc E. Pfetsch, Christian Puchert, Daniel Rehfeldt, Franziska Schlösser, Christoph Schubert, Felipe Serrano, Yuji Shinano, Jan Merlin Viernickel, Matthias Walter, Fabian Wegscheider, Jonas T. Witt, and Jakob Witzig. The SCIP Optimization Suite 6.0. ZIB-Report 18-26, Zuse Institute Berlin, 2018.

L. Grippo, F. Lampariello, and S. Lucidi. A nonmonotone line search technique for Newton's method. SIAM Journal on Numerical Analysis, 23(4):707–716, 1986.

L. Grippo, F. Lampariello, and S. Lucidi. A class of nonmonotone stabilization methods in unconstrained optimization. Numerische Mathematik, 59(1):779–805, 1991.

Computational Mathematics Group. HSL 2002 – a catalogue of subroutines. Technical report, STFC Rutherford Appleton Laboratory, Harwell Oxford, 2002.

R. A. Gutiérrez and N. V. Sahinidis. A branch-and-bound approach for machine selection in just-in-time manufacturing systems. International Journal of Production Research, 34(3):797–818, 1996.

P. T. Harker and J. S. Pang. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming, 48(1-3):161–220, 1990.

G. W. Harrison, T. F. Rutherford, and D. Tarr. Quantifying the Uruguay round. The Economic Journal, 107(444):1405–1430, 1997.

Alain Haurie and Jacek B. Krawczyk. Optimal charges on river effluent from lumped and distributed sources environmental modeling and assessment. Environmental Modeling & Assessment, 2(3):177–189, 1997.

J. Huang and J. S. Pang. Option pricing and linear complementarity. Journal of Computational Finance, 2(1):31–60, 1998.

Q. Huangfu and J. A. J. Hall. Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10(1):119–142, 2018.

P. J. Huber. Robust statistics. John Wiley & Sons, New York, 1981.

G. Infanger. DECIS User's Guide. 1590 Escondido Way, Belmont, CA 94002, 1997.

N. H. Josephy. Newton's method for generalized equations. Technical Summary Report 1965, Mathematics Research Center, University of Wisconsin, Madison, Wisconsin, 1979.

W. Karush. Minima of functions of several variables with inequalities as side conditions. Master's thesis, Department of Mathematics, University of Chicago, 1939.

George Karypis and Vipin Kumar. A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359–392, 1999.

Yoshiaki Kawajir, Carl Laird, and Andreas Wächter. Introduction to Ipopt: A tutorial for downloading, installing, and using Ipopt, 2087 edition, February 2012. https://github.com/coin-or/Ipopt.

J. E. Kelley. The cutting-plane method for solving convex programs. Journal of the Society for Industrial and Applied Mathematics, 8(4):703–712, 1960.

A. Khajavirad and N. V. Sahinidis. Convex envelopes of products of convex and component-wise concave functions. Journal of Global Optimization, 52(3):391–409, 2012.

A. Khajavirad and N. V. Sahinidis. Convex envelopes generated from finitely many compact convex sets. Mathematical Programming, 137(1-2):371–408, 2013.

A. Khajavirad, J. J. Michalek, and N. V. Sahinidis. Relaxations of factorable functions with convex-transformable intermediates. Mathematical Programming, 144(1-2):107–140, 2014.

Y. Kim and M.C. Ferris. Solving equilibrium problems using extended mathematical programming, 2017.

G. R. Kocis and I. E. Grossmann. Relaxation strategy for the structural optimization of process flowsheets. Industrial & Engineering Chemistry Research, 26(9):1869–1880, 1987.

Jacek B. Krawczyk and Stanislav Uryasev. Relaxation algorithms to find nash equilibria with economic applications. Environmental Modeling & Assessment, 5(1):63–73, 2000.

J. Kronqvist, A. Lundell, and T. Westerlund. The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming. Journal of Global Optimization, 64(2):249–272, 2016.

J. Kronqvist, D. E. Bernal, A. Lundell, and I. E. Grossmann. A review and comparison of solvers for convex minlp. Optimization and Engineering, 20(2):397–455, 2019.

H. W. Kuhn and A. W. Tucker. Nonlinear programming. In J. Neyman, editor, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pages 481–492, Berkeley and Los Angeles, 1951. University of California Press.

B. Lanz and T. F. Rutherford. Gtapingams: Multiregional and small open economy models. Journal of Global Economic Analysis, 1(2):1–77, 2016.

Y. Lebbah, C. Michel, and M. Rueher. A rigorous global filtering algorithm for quadratic constraints. Constraints, 10(1):47–65, 2005.

C. E. Lemke and J. T. Howson, Jr. Equilibrium points of bimatrix games. Journal of the Society for Industrial and Applied Mathematics, 12(2):413–423, 1964.

L. Liberti and C. C. Pantelides. Convex envelopes of monomials of odd degree. Journal of Global Optimization, 25(2):157–168, 2003.

L. Liberti and C. C. Pantelides. An exact reformulation algorithm for large nonconvex NLPs involving bilinear terms. Journal of Global Optimization, 36(2):161–189, 2006.

M.-L. Liu, N. V. Sahinidis, and J. P. Shectman. Planning of chemical process networks via global concave minimization. In I. E. Grossmann, editor, Global Optimization in Engineering Design, volume 9 of Nonconvex Optimization and Its Applications, pages 195–230. Springer, 1996.

A. Lundell and J. Kronqvist. On solving nonconvex MINLP problems with SHOT. In Le Thi H., Le H., and Pham Dinh T., editors, Optimization of Complex Systems: Theory, Models, Algorithms and Applications, volume 991 of Advances in Intelligent Systems and Computing. Springer, Cham., 2019.

A. Lundell and J. Kronqvist. Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT. Journal of Global Optimization, 2021.

A. Lundell and T. Westerlund. Convex underestimation strategies for signomial functions. Optimization Methods and Software, 24(4-5):505–522, 2009.

A. Lundell and T. Westerlund. Global optimization of mixed-integer signomial programming problems. In J. Lee and S. Leyffer, editors, Mixed Integer Nonlinear Programming, volume 154 of The IMA Volumes in Mathematics and its Applications, pages 349–369. Springer New York, 2012.

A. Lundell, J. Westerlund, and T. Westerlund. Some transformation techniques with applications in global optimization. Journal of Global Optimization, 43(2-3):391–405, 2009.

A. Lundell, J. Kronqvist, and T. Westerlund. The supporting hyperplane optimization toolkit: A polyhedral outer approximation based convex minlp solver utilizing a single branching tree approach. Technical report, Optimization Online, 2018.

Stephen J. Maher, Tobias Fischer, Tristan Gally, Gerald Gamrath, Ambros Gleixner, Robert Lion Gottwald, Gregor Hendel, Thorsten Koch, Marco E. Lübbecke, Matthias Miltenberger, Benjamin Müller, Marc E. Pfetsch, Christian Puchert, Daniel Rehfeldt, Sebastian Schenker, Robert Schwarz, Felipe Serrano, Yuji Shinano, Dieter Weninger, Jonas T. Witt, and Jakob Witzig. The SCIP Optimization Suite 4.0. ZIB Report 17-12, Zuse Institute Berlin, 2017.

C. D. Maranas and C. A. Floudas. Finding all solutions of nonlinearly constrained systems of equations. Journal of Global Optimization, 7(2):143–182, 1995.

C. D. Maranas and C. A. Floudas. Global optimization in generalized geometric programming. Computers & Chemical Engineering, 21(4):351–369, 1997.

J. Markusen and T. F. Rutherford. MPSGE: A user’s guide, February 2004. Lecture Notes Prepared for the UNSW Workshop.

L. Mathiesen. Computation of economic equilibria by a sequence of linear complementarity problems. In Alan S. Manne, editor, Economic Equilibrium: Model Formulation and Solution, volume 23 of Mathematical Programming Studies, pages 144–162. Springer, Berlin, Heidelberg, 1985.

L. Mathiesen. An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model: An example. Mathematical Programming, 37(1):1–18, 1987.

C. A. Meyer and C. A. Floudas. Convex envelopes for edge-concave functions. Mathematical Programming, 103(2):207–224, 2005.

R. Misener and C. A. Floudas. Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations. Mathematical Programming, 136(1):155–182, 2012.

R. Misener and C. A. Floudas. GloMIQO: Global Mixed-Integer Quadratic Optimizer. Journal of Global Optimization, 57(1):3–50, 2013.

R. Misener and C. A. Floudas. ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations. Journal of Global Optimization, 59(2-3):503–526, 2014.

R. Misener and C. A. Floudas. A framework for globally optimizing mixed-integer signomial programs. Journal of Optimization Theory and Applications, 161(3):905–932, 2014.

R. Misener, J. B. Smadbeck, and C. A. Floudas. Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2. Optimization Methods and Software, 30(1):215–249, 2015.

B. A. Murtagh and M. A. Saunders. Large-scale linearly constrained optimization. Mathematical Programming, 14(1):41–72, 1978.

B. A. Murtagh and M. A. Saunders. A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints. In A. G. Buckley and J.-L. Goffin, editors, Algorithms for Constrained Minimization of Smooth Nonlinear Functions, volume 16 of Mathematic Programming Studies, pages 84–117. Springer, Berlin, Heidelberg, 1982.

B. A. Murtagh and M. A. Saunders. Minos 5.5 user's guide. Technical Report SOL 83-20R, Department of Operations Research, Stanford University, Stanford, CA, 1983. Revised 1998.

B. A. Murtagh and M. A. Saunders. Minos user's guide. Technical Report SOL 83-20, Department of Operations Research, Stanford University, Stanford, CA, 1983.

J. Nocedal and S. J. Wright. Numerical Optimization. Springer Series in Operations Research. Springer, 1999.

Jorge Nocedal, Andreas Wächter, and Richard A. Waltz. Adaptive barrier strategies for nonlinear interior methods. SIAM Journal on Optimization, 19(4):1674–1693, 2008.

Ray Pörn and Tapio Westerlund. A cutting plane method for minimizing pseudo-convex functions in the mixed integer case. Computers & Chemical Engineering, 24(12):2655–2665, 2000.

I. Quesada and I. E. Grossmann. A global optimization algorithm for linear fractional and bilinear programs. Journal of Global Optimization, 6(1):39–76, 1995.

J. K. Reid. Fortran subroutines for handling sparse linear programming bases. Technical Report Report R8269, Atomic Energy Research Establishment, Harwell, England, 1976.

J. K. Reid. A sparsity-exploiting variant of the Bartels-Golub decomposition for linear programming bases. Mathematical Programming, 24(1):55–69, 1982.

L. M. Rios and N. V. Sahinidis. Portfolio optimization for wealth-dependent risk preferences. Annals of Operations Research, 177(1):63–90, 2010.

S. M. Robinson. A quadratically-convergent algorithm for general nonlinear programming problems. Mathematical Programming, 3(1):145–156, 1972.

S. M. Robinson. Normal maps induced by linear transformations. Mathematics of Operations Research, 17(3):691–714, 1992.

R. T. Rockafellar. Linear-quadratic programming and optimal control. SIAM Journal on Control and Optimization, 25(3):781–814, 1987.

R. T. Rockafellar. Lagrange multipliers and optimality. SIAM Review, 35(2):183–238, 1993.

R. T. Rockafellar. Extended nonlinear programming. In Gianni Di Pillo and Franco Giannessi, editors, Nonlinear Optimization and Related Topics, volume 36 of Applied Optimization, pages 381–399. Springer, Boston, MA, 1999.

T. F. Rutherford. Extensions of GAMS for complementarity problems arising in applied economic analysis. Journal of Economic Dynamics and Control, 19(8):1299–1324, 1995.

T. F. Rutherford. Applied general equilibrium modeling with mpsge as a gams subsystem: An overview of the modeling framework and syntax. Computational Economics, 14(1-2):1–46, 1999.

H. S. Ryoo and N. V. Sahinidis. Global optimization of nonconvex NLPs and MINLPs with applications in process design. Computers & Chemical Engineering, 19(5):551–556, 1995.

H. S. Ryoo and N. V. Sahinidis. A branch-and-reduce approach to global optimization. Journal of Global Optimization, 8(2):107–138, 1996.

H. S. Ryoo and N. V. Sahinidis. Analysis of bounds for multilinear functions. Journal of Global Optimization, 19(4):403–424, 2001.

H. S. Ryoo and N. V. Sahinidis. Global optimization of multiplicative programs. Journal of Global Optimization, 26(4):387–418, 2003.

N. V. Sahinidis and M. Tawarmalani. Applications of global optimization to process and molecular design. Computers & Chemical Engineering, 24(9-10):2157–2169, 2000.

N. V. Sahinidis and M. Tawarmalani. Accelerating branch-and-bound through a modeling language construct for relaxation-specific constraints. Journal of Global Optimization, 32(2):259–280, 2005.

N. V. Sahinidis, M. Tawarmalani, and M. Yu. Design of alternative refrigerants via global optimization. AIChE Journal, 49(7):1761–1775, 2003.

N. V. Sahinidis. BARON: A general purpose global optimization software package. Journal of Global Optimization, 8(2):201–205, 1996.

N. V. Sahinidis. Global optimization and constraint satisfaction: The branch-and-reduce approach. In Ch. Bliek, Ch. Jermann, and A. Neumaier, editors, Global Optimization and Constraint Satisfaction, volume 2861 of Lecture Notes in Computer Science, pages 1–16. Springer, 2003.

Olaf Schenk and Klaus Gärtner. Solving unsymmetric sparse systems of linear equations with pardiso. Journal of Future Generation Computer Systems, 20(3):475–487, 2004.

Olaf Schenk and Klaus Gärtner. On fast factorization pivoting methods for sparse symmetric indefinite systems. Electronic Transactions on Numerical Analysis, 23:158–179, 2006.

J. P. Shectman and N. V. Sahinidis. A finite algorithm for global minimization of separable concave programs. Journal of Global Optimization, 12(1):1–36, 1998.

H. D. Sherali and W. P. Adams. A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, volume 31 of Nonconvex Optimization and Its Applications. Springer, Boston, MA, 1999.

H. D. Sherali and A. Alameddine. A new reformulation-linearization technique for bilinear programming problems. Journal of Global Optimization, 2(4):379–410, 1992.

H. D. Sherali and C. H. Tuncbilek. A reformulation-convexification approach for solving nonconvex quadratic-programming problems. Journal of Global Optimization, 7(1):1–31, 1995.

H. D. Sherali and C. H. Tuncbilek. New reformulation linearization/convexification relaxations for univariate and multivariate polynomial programming problems. Operations Research Letters, 21(1):1–9, 1997.

H. Sherali, E. Dalkiran, and L. Liberti. Reduced RLT representations for nonconvex polynomial programming problems. Journal of Global Optimization, 52(3):447–469, 2012.

Claus Still and Tapio Westerlund. Extended cutting plane algorithm. In C. A. Floudas and P. Pardalos, editors, Encyclopedia of Optimization, pages 593–601. Kluwer Academic Publishers, 2001.

F. Tardella. On the existence of polyhedral convex envelopes. In C. A. Floudas and P. M. Pardalos, editors, Frontiers in Global Optimization, volume 74 of Nonconvex Optimization and Its Applications, pages 563–573. Kluwer Academic Publishers, 2004.

F. Tardella. Existence and sum decomposition of vertex polyhedral convex envelopes. Optimization Letters, 2(3):363–375, 2008.

F. Tardella. On a class of functions attaining their maximum at the vertices of a polyhedron. Discrete Applied Mathematics, 22(2):191–195, 1988/89.

M. Tawarmalani and N. V. Sahinidis. Semidefinite relaxations of fractional programs via novel convexification techniques. Journal of Global Optimization, 20(2):133–154, 2001.

M. Tawarmalani and N. V. Sahinidis. Convex extensions and envelopes of lower semi-continuous functions. Mathematical Programming, 93(2):247–263, 2002.

M. Tawarmalani and N. V. Sahinidis. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, volume 65 of Nonconvex Optimization and Its Applications. Kluwer Academic Publishers, 2002.

M. Tawarmalani and N. V. Sahinidis. Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Mathematical Programming, 99(3):563–591, 2004.

M. Tawarmalani and N. V. Sahinidis. A polyhedral branch-and-cut approach to global optimization. Mathematical Programming, 103(2):225–249, 2005.

M. Tawarmalani, S. Ahmed, and N. V. Sahinidis. Global optimization of 0-1 hyperbolic programs. Journal of Global Optimization, 24(4):385–416, 2002.

M. Tawarmalani, S. Ahmed, and N. V. Sahinidis. Product disaggregation in global optimization and relaxations of rational programs. Optimization and Engineering, 3(3):281–303, 2002.

P. Tseng. Growth behavior of a class of merit functions for the nonlinear complementarity problem. Journal of Optimization Theory and Applications, 89(1):17–37, 1996.

M. Türkay and I. E. Grossmannn. Logic-based MINLP algorithms for the optimal synthesis of process networks. Computers & Chemical Engineering, 20(8):959–978, 1996.

J. G. VanAntwerp, R. D. Braatz, and N. V. Sahinidis. Globally optimal robust control for systems with time-varying nonlinear perturbations. Computers & Chemical Engineering, 21, Supplement:S125–S130, 1997.

J. G. VanAntwerp, R. D. Braatz, and N. V. Sahinidis. Globally optimal robust process control. Journal of Process Control, 9(5):375–383, 1999.

A. Vecchietti and I. E. Grossmannn. LOGMIP: a disjunctive 0-1 non-linear optimizer for process system models. Computers & Chemical Engineering, 23(4-5):555–565, 1999.

A. Vecchietti, S. Lee, and I. E. Grossmannn. Modeling of discrete/continuous optimization problems: Characterizaton and formulations of disjunctions and their relaxations. Computers & Chemical Engineering, 27(3):433–448, 2003.

Stefan Vigerske. Decomposition of Multistage Stochastic Programs and a Constraint Integer Programming Approach to Mixed-Integer Nonlinear Programming. PhD thesis, Humboldt-Universität zu Berlin, 2013.

J. Viswanathan and I. E. Grossmann. A combined penalty function and outer approximation method for minlp optimization. Computers & Chemical Engineering, 14(7):769–782, 1990.

Andreas Wächter and Lorenz T. Biegler. Line search filter methods for nonlinear programming: Local convergence. SIAM Journal on Optimization, 16(1):32–48, 2005.

Andreas Wächter and Lorenz T. Biegler. Line search filter methods for nonlinear programming: Motivation and global convergence. SIAM Journal on Optimization, 16(1):1–31, 2005.

Andreas Wächter and Lorenz T. Biegler. On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming, 106(1):25–57, 2006. http://github.com/coin-or/Ipopt.

Andreas Wächter. An Interior Point Algorithm for Large-Scale Nonlinear Optimization with Applications in Process Engineering. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, January 2002.

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban. An interior algorithm for nonlinear optimization that combines line search and trust region steps. Mathematical Programming, 107(3):391–408, 2006.

Tapio Westerlund and Frank Petterson. An extended cutting plane method for solving convex MINLP problems. Computers & Chemical Engineering, 19(suppl.):131–136, 1995.

Tapio Westerlund and Ray Pörn. Solving pseudo-convex mixed integer optimization problems by cutting plane techniques. Optimization and Engineering, 3(3):253–280, 2002.

Tapio Westerlund, Hans Skrifvars, Iiro Harjunkoski, and Ray Pörn. An extended cutting plane method for solving a class of non-convex minlp problems. Computers & Chemical Engineering, 22(3):357–365, 1998.

H. P. Williams. Model Building in Mathematical Programming. Wiley, 4th edition, 1999.

P. Wolfe. The reduced gradient method. RAND Corporation, 1962.

S. J. Wright. Primal-Dual Interior-Point Methods. Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1997.

Roland Wunderling. Paralleler und objektorientierter Simplex-Algorithmus. PhD thesis, Technische Universität Berlin, 1996. http://soplex.zib.de.

Maryam Yashtini and Alaeddin Malek. Solving complementarity and variational inequalities problems using neural networks. Applied Mathematics, 190(1):216–230, 2007.

K. Zorn and N. V. Sahinidis. Computational experience with applications of bilinear cutting planes. Industrial & Engineering Chemistry Research, 52(22):7514–7525, 2013.

K. Zorn and N. V. Sahinidis. Global optimization of general non-convex problems with intermediate bilinear substructures. Optimization Methods and Software, 29(3):442–462, 2014.

K. Zorn and N. V. Sahinidis. Global optimization of general nonconvex problems with intermediate polynomial substructures. Journal of Global Optimization, 59(2-3):673–693, 2014.