# MINLP Resources

Sections:

## Lectures and Tutorials

## Conferences

## Libraries

## Research Projects

## Modeling Systems

## Solvers

## LP |
## MILP |
## NLP |
## MINLP |
## GDP |

## Bibliography

- Abhishek, K., S. Leyffer, J.Linderoth (2010) FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs INFORMS Jounal on Computing, Published online in Articles in Advance, March 11, 2010, DOI: 10.1287/ijoc.1090.0373
- Adjiman, C. S.; Androulakis, I. P.; Floudas, C. A. (2000) Global optimization of mixed-integer nonlinear problems. AIChE Journal 16, 1769.
- Al-Khayyal F.A. & Falk J. E. (1983) Jointly Constrained Biconvex Programming. Math. of Operation Research, 8,2, 273-286
- Balas, E. (1979) Disjunctive Programming . Annals of Discrete Mathematics 5 (1979) 3-51
- Balas, E. (1985) Disjunctive Programming and a hierarchy of relaxations for discrete optimization problems. SIAM Journal on Algebraic and Discrete Methods, 6, 466-486.
- Bao, X., N. V. Sahinidis, and M. Tawarmalani, Multiterm polyhedral relaxations for nonconvex, quadratically-constrained quadratic programs, Optimization Methods and Software, 24, 485-504, 2009.
- Belotti, P., C. Kirches, S. Leyffer, J. Linderoth, J. Luedtkea and A. Mahajana, “Mixed-integer Nonlinear Optimization,” Acta Numerica, 22, 1-131(2013).
- Belotti, Pietro, Sonia Cafieri, Jon Lee, and Leo Liberti. Feasibility-based bounds tightening via fixed points. In: Proceedings of the 4th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2010), W. Wu and O. Daescu (Eds.), Lecture Notes in Computer Science, Vol. 6508, pp. 65–76, 2010. Springer-Verlag.
- Belotti, Pietro, Jon Lee, Leo Liberti, Francois Margot, Andreas Waechter. Branching and bounds tightening techniques for non-convex MINLP, Optimization Methods and Software 24 (2009), 597--634
- Benders J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238-252
- Bergamini, M. L.; Aguirre, P.; Grossmann, I. E. (2005) Logic-based Outer Approximation for Globally Optimal Synthesis of Process Networks, Computers and Chemical Engineering, 29, 1914-1933.
- Bergamini, M.L., I.E. Grossmann, N. Scenna and P. Aguirre (2008) An Improved Piecewise Outer-Approximation Algorithm for the Global Optimization of MINLP Models Involving Concave and Bilinear Terms, Computers and Chemical Engineering 32, 477-493.
- Berstein, Yael, Jon Lee, Shmuel Onn and Robert Weismantel. Nonlinear optimization for matroid intersection and extensions, Mathematical Programming, 2010, Volume 124, Numbers 1-2, Pages 233-253.
- Bonami, Pierre, Jon Lee, Sven Leyffer, Andreas Waechter. On branching rules for convex mixed-integer nonlinear optimization. ACM J. Exp. Algorithmics 18 (2013), Article 2.6, 31 pp
- Bonami, P., Kilinc, M., Linderoth, J. T. "Algorithms and software for convex mixed integer nonlinear programs." Mixed Integer Nonlinear Programming. Springer New York, 1-39 (2012).
- Bonami,P., Jon Lee, Sven Leyffer, Andreas Waechter. More Branch-and-Bound Experiments in Convex Nonlinear Integer Programming. September, 2011. Optimization Online: http://www.optimization-online.org/DB_HTML/2011/09/3191.html
- Bonami, P., L.T. Biegler, A.R. Conn, G. Cornuejols, I.E. Grossmann, C.D. Laird, J. Lee, A. Lodi, F. Margot, N. Sawaya, A. Waechter (2008) An algorithmic framework for convex mixed integer nonlinear programs,
*Discrete Optimization*5, 186-204. - Bonami, P., John Forrest, Jon Lee and Andreas Waechter. Rapid development of an MINLP solver with COIN-OR, Optima, 75:1-5, December 2007.
- Borchers, B., J.E. Mitchell (1994) An improved branch and bound algorithm for mixed integer nonlinear programs, Computers & Operations Research, 21, 359-367
- Bragalli, C., Claudia D'Ambrosio, Jon Lee, Andrea Lodi, Paolo Toth. An MINLP model and solution method for a water-network optimization problem. Algorithms - ESA 2006 (14th Annual European Symposium. Zurich, Switzerland, September 2006, Proceedings), Y. Azar and T. Erlebach, Eds., pages 696-707. Springer, 2006.
- Bragalli, C., Claudia D'Ambrosio, Jon Lee, Andrea Lodi, Paolo Toth. Water Network Design by MINLP, IBM Research Report RC24495, 02/2008.
- Cafieri, Sonia, Jon Lee and Leo Liberti, Comparison of convex relaxations of quadrilinear terms. Journal of Global Optimization, Vol. 47, No. 4 (2010), 661-685.
- Chachuat, B.; Singer, A. B.; Barton, P. I. (2005) Global Mixed-Integer Dynamic Optimization, AICHE Journal, 51, 2235-2253
- Coppersmith, Don, Jon Lee and Janny Leung. A polyhedron for products of linear functions in 0/1 variables. IBM Research Report RC21568, September 1999. Revised, with Oktay Günlük, November 2003. IMA book series, to appear.
- Claudia D'Ambrosio, Jon Lee, Andreas Wächter. An algorithmic framework for MINLP with separable non-convexity, To appear in: Mixed-Integer Nonlinear Optimization: Algorithmic Advances and Applications (IMA Book Series, Springer).
- D'Ambrosio, C., A. Frangioni, L. Liberti, A. Lodi, A storm of Feasibility Pumps for Nonconvex MINLP, Mathematical Programming B, 136:229-231, 2012.
- D'Ambrosio, Claudia, Jon Lee, Andreas Wächter. A global-optimization algorithm for mixed-integer nonlinear programs having separable non-convexity. Proceedings of ESA 2009, Fiat, Amos; Sanders, Peter (Eds.), Lecture Notes in Computer Science, Volume 5757, pp. 107-118.
- D'Ambrosio, C., J. Lee, A. Wächter, An algorithmic framework for MINLP with separable non-convexityAn algorithmic framework for MINLP with separable non-convexity, The IMA Volumes in Mathematics and its Applications, Volume 154, pp. 315-347, Springer, 2012.
- Dakin, R.J. (1965) A tree-search algorithm for mixed integer programming problems, The Computer Journal, 8, 250-255.
- Duran, M. A.; Grossmann, I. E. (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming 36, (3), 307.
- Falk, J. E.; Hoffman, K. R. (1976) A Successive Underestimation Method for Concave Minimization Problems. Mathematics of Operations Research 1, (3), 251.
- Fletcher, R.; Leyffer, S. (1994) Solving Mixed Integer Nonlinear Programs by Outer Approximation, Mathematical Programming, 66, 327-349
- Floudas, C. A. (2000) Deterministic Global Optimization: Theory, Methods and Applications. Kluwer Academic Publishers : Dordrecht, The Netherlands
- Gauthier, J.M. and G. Ribière (1977) Experiments in mixed-integer linear programming using pseudo-costs,

Mathematical Programming, 12, 26-47 - Geoffrion, A. M. (1972) Generalized Benders Decomposition. Journal of Optimization Theory and Applications 10, (4), 237.
- Giacomo Nannicini, Pietro Belotti, Jon Lee, Jeff Linderoth, Francois Margot, Andreas Waechter. A Probing Algorithm for MINLP with Failure Prediction by SVM, In: CPAIOR 2011, LNCS Volume 6697, T. Achterberg and J.C. Beck (Eds.), pp. 154-169, 2011.
- Grossmann, I.E. and F. Trespalacios, “Systematic Modeling of Discrete-Continuous Optimization Models through Generalized Disjunctive Programming,” AIChE J. 59, 3276-3295 (2013).
- Grossmann, I. E. (2002) Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques. Optimization and Engineering 3, 227.
- Gunluk, O., Jon Lee and Robert Weismantel. MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL, IBM Research Report RC24213, 03/2007.
- Gupta, O.K., A. Ravindran (1985) Branch and Bound Experiments in Convex Nonlinear Integer Programming, Management Science, 31, 1533-1546
- Hemmecke,R., Mathias Köppe, Jon Lee, Robert Weismantel. Nonlinear integer programming. In: M. Jünger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958–2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2010, ISBN 3540682740, pp. 561-618.
- Karuppiah, R. and I.E. Grossmann (2008) A Lagrangean based Branch-and-Cut algorithm for global optimization of nonconvex Mixed-Integer Nonlinear Programs with decomposable structures, Journal of Global Optimization 41, 163.
- Kesavan, P.; Allgor, R. J.; Gatzke, E. P.; Barton, P. I. (2004), Outer Approximation Algorithms for Separable Nonconvex Mixed-Integer Nonlinear Programs. Mathematical Programming 100, (3), 517.
- Lee.J. and S. Leyffer (Eds). Mixed Integer Nonlinear Programming, in The IMA Volumes in Mathematics and its Applications, Vol. 154, Springer, 2012.
- Lee, J.. On the boundary of tractability for nonlinear discrete optimization. Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization. S. Cafieri, A. Mucherino, G. Nannicini, Tarissan,F., L. Liberti, Eds. Pages 373-383.
- Lee,J., Shmuel Onn, Robert Weismantel. Intractability of approximate multi-dimensional nonlinear optimization on independence systems. Discrete Mathematics, Volume 311, Issues 8-9, 6 May 2011, Pages 780-783.
- Lee,J., Shmuel Onn, Lyubov Romanchuk, Robert Weismantel. The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions, IBM Research Report RC24999, 05/2010. To appear in: Mathematical Programming, Series B.
- Jon Lee and Sven Leyffer, Editors. "Mixed Integer Nonlinear Programming". The IMA Volumes in Mathematics and its Applications, Vol. 154. 1st Edition., 2011, X, 660 p. 1 illus. Hardback, ISBN 978-1-4614-1926-6. To appear: November 2011.
- Jon Lee, Shmuel Onn, Lyubov Romanchuk, Robert Weismantel. The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions, IBM Research Report RC24999, 05/2010. To appear in: Mathematical Programming, Series B.
- Jon Lee, Shmuel Onn, Robert Weismantel. Intractability of approximate multi-dimensional nonlinear optimization on independence systems.Discrete Mathematics, Volume 311, Issues 8-9, 6 May 2011, Pages 780-783.
- Kolodziej, S.P., P. Castro and I.E. Grossmann, “Global Optimization of Bilinear Programs with a Multiparametric Disaggregation Technique,” Journal of Global Optimization 57, 1039–1063 (2013).
- Kolodziej, S.P., P. Castro and I.E. Grossmann, “Global Optimization of Bilinear Programs with a Multiparametric Disaggregation Technique,” to appear in Journal of Global Optimization (2012).
- Lee, Jon, Shmuel Onn and Robert Weismantel, Approximate nonlinear optimization over weighted independence systems. SIAM J. on Discrete Mathematics, Vol 23, No. 4 (2009), 1667-1681.
- Lee, J. (2007) "In situ column generation for a cutting-stock problem," Computers & Operations Research 34, (8), 2345-2358.
- Lee, J., Shmuel Onn, Robert Weismantel. On test sets for nonlinear integer maximization. Operations Research Letters 36:439-443, 2008.
- Lee, J. Mixed Integer Nonlinear Programming: Some Modeling and Solution Issues, in"Business Optimization", IBM Journal of Research and Development, 51(3/4): 489-497, 2007.
- Lee, S. and I.E. Grossmann, "New Algorithms for Nonlinear Generalized Disjunctive Programming,” Computers and Chemical Engineering, 24, pp.2125- 2141 (2000).
- Lee, S. and I.E. Grossmann (2001) "A Global Optimization Algorithm for Nonconvex Generalized Disjunctive Programming and Applications to Process Systems, " Computers and Chemical Engineering 25, 1675-1697.
- Lee, S. and I.E. Grossmann (2003) "Global Optimization of Nonlinear Generalized Disjunctive Programming with Bilinear Equality Constraints: Applications to Process Networks," Computers and Chemical Engineering 27,1557-1575.
- Leyffer, S. (2003) Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming, Computational Optimization and Applications, 18, 295-309
- Leyffer, S. (2001)Integrating SQP and branch and bound for mixed integer nonlinear programming. Computational Optimization and Applications 18, 295.
- Liu, M. L., N. V. Sahinidis, and J. P. Shectman, Planning of chemical process networks via global concave minimization, Chapter 7, pp. 195-230, in I. E. Grossmann (ed.), Global Optimization in Engineering Design, Kluwer Academic Publishers, Dordrecht, MA, 1996.
- McCormick, G. P. (1976) Computability of global solutions to factorable nonconvex programs. Part I. Convex underestimating problems. Mathematical Programming, 10, 146-175.
- Nannicini, G., Pietro Belotti, Jon Lee, Jeff Linderoth, Francois Margot, Andreas Waechter. A Probing Algorithm for MINLP with Failure Prediction by SVM, In: CPAIOR 2011, LNCS Volume 6697, T. Achterberg and J.C. Beck. (Eds.), pp. 154-169, 2011.
- Quesada, I.; Grossmann, I. E. (1992) An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Computers & Chemical Engineering 16, 937.
- Quesada, I.; Grossmann, I. E. (1995) A Global Optimization Algorithm for Linear Fractional and Bilinear Programs. Journal of Global Optimization 6, 39.
- Raman, R. and I.E. Grossmann, "Modeling and Computational Techniques for Logic Based Integer Programming," Computers and Chemical Engineering, 18, 563 (1994).
- Ruiz, J.P. and I.E. Grossmann, “A hierarchy of relaxations for nonlinear convex generalized disjunctive programming,” European Journal of Operational Research 218, 38–47 (2012).
- Ruiz, J.P. and I.E. Grossmann, “Using redundancy to strengthen the relaxation for the global optimization of MINLP problems,” Computers and Chemical Engineering 35 2729– 2740 (2011).
- Ruiz, J.P. and I.E. Grossmann, “A hierarchy of relaxations for nonlinear convex generalized disjunctive programming,” European Journal of Operational Research 218, 38–47 (2012).
- Ruiz, J.P. and I.E. Grossmann, “Strengthening of Lower Bounds in the Global Optimization of Bilinear and Concave Generalized Disjunctive Programs,” Computers and Chemical Engineering 34 914–930 (2010).
- Ruiz, J.P. and I.E. Grossmann, “Exploiting Vector Space Properties to Strengthen the Relaxation of Bilinear Programs Arising in the Global Optimization of Process Networks,” Optimization Letters, 5, 1-11 (2011).
- Ryoo, H. S. and N. V. Sahinidis, Global optimization of multiplicative programs, Journal of Global Optimization, 26(4), 387-418, 2003.

- Ryoo, H. S. and N. V. Sahinidis, Analysis of bounds for multilinear functions, Journal of Global Optimization, 19(4), 403-424, 2001.
- Ryoo, H. S. and Sahinidis, N. V. (1996) A branch-and-reduce approach to global optimization. Journal of Global Optimization 8, (2), 107.

- Ryoo, H. S. and N. V. Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Computers & Chemical Engineering, 19(5), 551-566, 1995.
- Sahinidis, N. V. and M. Tawarmalani, Accelerating branch-and-bound through a modeling language construct for relaxation-specific constraints, Journal of Global Optimization, 32, 259-280, 2005.
- Sahinidis, N. V., Global optimization and constraint satisfaction: The branch-and-reduce approach, pp. 1-16 in C. Bliek, C. Jermann, and A. Neumaier (eds.), Global Optimization and Constraint Satisfaction, Lecture Notes in Computer Science, Vol. 2861, Springer, Berlin, 2003.
- Sahinidis, N. V. (1996) BARON: A general purpose global optimization software package. Journal of Global Optimization 8, (2), 201.
- Sawaya, N. and I.E. Grossmann, “A hierarchy of relaxations for linear generalized disjunctive programming,” European Journal of Operational Research 216 70-82 (2012).
- Sawaya, N. and I.E. Grossmann, “Reformulations, Relaxations and Cutting Planes for Linear Generalized Disjunctive Programming,” European Journal of Operational Research 216 70-82 (2012).
- Sawaya, N.W. and I.E. Grossmann, “Computational Implementation of Non-Linear Convex Hull Reformulation,” Computers & Chemical Engineering, 31, 856-866 (2007).
- Saxena, A., Pierre Bonami and Jon Lee. Disjunctive cuts for non-convex mixed integer quadratically constrained programs, In: Integer programming and combinatorial optimization (Bertinoro, 2008), A. Lodi, A. Panconesi, and G. Rinaldi, Eds., Lecture Notes in Computer Science volume 5035, pp. 17-33. Springer-Verlag Berlin Heidelberg, 2008.
- Saxena, A., Pierre Bonami and Jon Lee. Convex Relaxations of Non-Convex Mixed Integer Quadratically Constrained Programs: Extended Formulations, IBM Research Report RC24621, 08/2008. To appear in Mathematical Programming.
- Saxena, A., Pierre Bonami and Jon Lee. Convex Relaxations of Non-Convex Mixed Integer Quadratically Constrained Programs: Projected Formulations, IBM Research Report RC24695, 11/2008.
- Shectman, J. P. and N. V. Sahinidis, A finite algorithm for global minimization of separable concave programs, Journal of Global Optimization, 12(1), 1-36, 1998.
- Smith, E. M. B.; Pantelides, C. C. (1999) A symbolic reformulation/spatial branch and bound algorithm for the global optimization of nonconvex MINLPs. Computers & Chemical Engineering 23, 457.
- Tawarmalani, M. and N. V. Sahinidis, A polyhedral branch-and-cut approach to global optimization, Mathematical Programming, Ser. B, 103, 225-249, 2005.

- Tawarmalani, M.; Sahinidis, N. V. (2004) Global optimization of mixed-integer nonlinear programs: A theoretical and computational study. Mathematical Programming 99, 563.
- Tawarmalani, M., Sahinidis, N. (2002) Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming. , Kluwer Academic Publishers
- Tawarmalani, M., S. Ahmed, and N. V. Sahinidis, Product disaggregation and relaxations of mixed-integer rational programs, Optimization and Engineering, 3(3), 281-303, 2002.

- Tawarmalani, M., S. Ahmed, and N. V. Sahinidis, Global optimization of 0-1 hyperbolic programs, Journal of Global Optimization, 24(4), 385-417, 2002.
- Tawarmalani, M. and N. V. Sahinidis, Convex extensions and envelopes of lower semi-continuous functions, Mathematical Programming, Ser. A, 93(2), 247-263, 2002.

- Tawarmalani, M. and N. V. Sahinidis, Semidefinite relaxations of fractional programs via novel convexification techniques, Journal of Global Optimization, 20(2), 137-158, 2001.
- Trespalacios, F. and I.E. Grossmann, “Algorithmic approach for improved mixed-integer reformulations of convex Generalized Disjunctive Programs,” INFORMS Journal of Computing 27, 59-74 (2014).
- Trespalacios, F. and I.E. Grossmann, “Review of mixed-integer nonlinear and generalized disjunctive programming methods,” Chemie Ingenieur Technik 86, 991-1012 (2014).
- Turkay, M. and I.E. Grossmann, "Logic-Based MINLP Algorithms For the Optimal Synthesis Of Process Networks," Computers and Chemical Engineering , 20, 959- 978 (1996).
- Vecchietti, A., Lee, S. , Grossmann, I. E. (2003) Modeling of discrete/continuous optimization problems: characterization and formulation of disjunctions and their relaxations. Computers and Chemical Engineering 27, 433-448
- Viswanathan, J.; Grossmann, I. E. (1990) A combined penalty-function and outer-approximation method for MINLP optimization. Computers & Chemical Engineering 14, (7), 769.
- Westerlund, T.; Pettersson, F. (1995) A cutting plane method for solving convex MINLP problems. Computers & Chemical Engineering 19, S131.
- Westerlund T. and Paorn R. (2002). Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques. Optimization and Engineering, 3, 253-280.Zamora, J.M. and I.E. Grossmann (1999) "A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms," Journal of Global Optimization 14, 217-249.
- You, F., P.M. Castro and I.E. Grossmann, “Dinkelbach’s Algorithm as an Efficient Method for Solving a Class of MINLP Models for Large-Scale Cyclic Scheduling Problems,” Computers and Chemical Engineering, 33, 1879-1889 (2009).
- Zamora, J.M. and I.E. Grossmann, "A Branch and Contract Algorithm for Problems with Concave Univariate, Bilinear and Linear Fractional Terms," Journal of Global Optimization 14, 217-249 (1999).