A. Frangioni and C. Gentile, 2006. Perspective cuts for a class of convex 0-1 mixed integer programs. Mathematical Programming, 106:225–236.
A.H. Land, A.G. Doig, 1960. An automatic method of solving discrete programming problems, Econometrica 28, 497-520.
A.M. Geoffrion, 1972. A Generalized Benders Decomposition, J.Op-tim. Theory Appl., vol. 10 (4), pp. 237–260.
A. W¨achter and L. T. Biegler, 2006. On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming, 106:25–57.
C.A. Floudas, 2000. Deterministic Global Optimization: Theory, Methods and Applications, Nonconvex Optimization And Its Applications series, 37, Kluwer Academic Publishers, Boston MA.
C. Bragalli, C. D’Ambrosio, J. Lee, A. Lodi, and P. Toth, 2006. An MINLP solution method for a water network problem. In Y. Azar and T. Erlebach, editors, Algorithms – ESA 2006, volume 4168 of Lecture Notes in Computer Science, pages 696–707. Springer–Verlag, Berlin Heidelberg.
C. D’Ambrosio, A. Frangioni, L. Liberti, A.Lodi, 2010. Experiments with a Feasibility Pump approachfor nonconvex MINLPs. In: P. Festa(ed) Proceedings of the 9th Synposiumon Experimental Algorithms (SEA 2010), Lecture Notes in Computer Science, Springer, Berlin, vol. 6049.
C. D’Ambrosio, A. Frangioni, L. Liberti, A. Lodi, 2012. A storm of Feasibility Pump for non-convex MINLP. Math. Program. Ser. B, vol 136(2), 375-402.
D. Bertsimas and R. Weismantel, 2005. Optimization over Integers. Dynamic Ideas, Belmont, Massachusetts, January.
E. Balas and J.B. Mazzola, 1984. “Nonlinear 0 − 1 programming: II. Dominance relations and algorithms”, Mathematical Programming 30, 22–45.
E.M.B. Smith, C.C. Pantelides, 1997. Global optimisation of non-convex MINLPs. Comput. Chem. Eng. 21, S791.
Gharibi, W. Improved Balas and Mazzola, 2012. Liniearization for Quadratic with Application in a New Cutting Plane Algorithm. Arxiv: 1204. 4829 VI.
G.L. Nemhauser and L.A. Wolsey, 1988. Integer and Combinatorial Optimization.
JohnWiley and Sons, New York.
G.P. McCormick, 1976. Computability of global solutions to factorable nonconvex programs. part I. Convex underestimating problems. Math.
Program. 10, 146-175.
G. Nannicini and P. Belotti, 2009 Local Branching for MINPs.Technical Report workingpaper, CMU.
G. Nannicini, P. Belotti, 2009. Rounding-based heuristics for non-convex MINLPs. In: P. Bonami, L. Liberti, A. Miller, A. Sartenear (eds).
Proceedings of the European Workshop on MINLP. CIRM, Marseille, France.
H.E. Scarf, 1986. Testing for Optimality in the Absence of Convexity. In: W. P.
Heller, R. M Starr and D. A. Starett (Eds) Cambridge University Press, pp.
117-134.
H. Mawengkang and B. A Murtagh, 1986. Solving Nonlinear Integer Programs with Large-Scale Optimization Software. Annals of Operations Research, pp. 5425-437.
H. Mawengkang, 1997, An Improved Search Algorithm for Solving Mixed-Integer Nonlinear Programming Problem. Proceeding of the 4th Int.
Meeting Decision Sciences Institute, Sydney, Australia, pp 709-711.
H.S. Ryoo, N.V. Sahinidis, 1995. Global optimization of non-convex NLPs and Kluwer Academic Publishers, Netherlands, vol. 3 (4).
I. Nowak, H. Alperin, and S. Vigerske, 2003. Lago – an object oriented library for solving minlps. In Global Optimization and Constraint Sarisfaction, volume 2861 of Lecture Notes in Computer Science, pages 32–42.
Springer, Berlin Heidelberg.
I. Nowak, 2003. LaGO: A Lagrangian Global Optimizer, [wwwhttp://www-iam.mathematik.hu-berlin.de/˜eopt/index en.html].
I. Quesada and I.E. Grossmann, 1992. An LP/NLP Based Branch and Bound Algorithm for Convex MINLP Optimization Problems, Computers Chem.
Eng., 16 (10/11), pp. 937–947.
K. Abhishek, 2008. Topics in Mixed Integer Nonlinear Programming. PhD thesis, Lehigh University.
L. Liberti, 2007. Compact Linearization for binary quadratic problems. 4OR, vol.
5(3), 231-245.
L. Liberti, N. Miladenovie, G. Nannicini, 2011. A Recipe for Finding Good Solutions to MINLPs. Mathematical Programming Computation.
L. Liberti, G. Nannicini, N. Mladenovic, 2009. A good recipe for solving MINLPs. In: V. Maniezzo, T. Stutzle, S.Voss(eds.) Metaheuristics:
Hybridizing metaheuristics and Mathematical Programming. Annals of Information Systems, Springer, vol. 10, pp. 231-245.
M.A. Duran and I. E Grossmann, 1986. An Outer-Approximation Algorithm For a class of Mixed-Integer Nonlinear Programs, Mathematical Programming, 36: 307.
M. Carri´on and J. M. Arroyo, 2006. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Transactions on Power Systems, 21:1371–1378.
M. Fischetti, F. Glover, A. Lodi, 2005. The Feasibility Pump. Mathematical Programming, vol. A 104(1), pp. 91-104.
M.R. Bussieck, A.S. Drud, and A. Meeraus, 2002. MINLPLib - A Collection of Test Models for Mixed-Integer Nonlinear Programming, INFORMS J.
Comput., to appear.
M. Tawarmalani, and N.V. Sahinidis, 2002. Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming:
Theory, Algorithms, Software, and Applications, Nonconvex Optimization And Its Applications series, 65, Kluwer Academic Publishers, Boston MA.
M. Tawarmalani, and N.V. Sahinidis, 2004. Global optimization of mixed-integer nolinear programs: a theoretical and computational study. Math. Program.
99, 563-591.
M. Tawarmalani, and N.V. Sahinidis, 2005. A polyhedral branch-and-cut approach to global optimization. Math. Program. 103, 225-249.
O.K. Gupta and A. Ravindran, 1985. Branch and Bound Experiments in Convex Nonlinear Integer Programming, Manage Sci., vol. 31 (12), pp. 1533–
1546.
P. Belotti, J. Lee, L. Liberti, F. Margot, A. Wachter, 2009. Branching and Bounds Tightening Techniques for non-convex MINLP, Optimization Methods and Software, vol. 24(4) 597-634.
P. Bonami, G. Cornu´ejols, A. Lodi, and F. Margot. A feasibility pump for mixed integer nonlinear programs. Mathematical Programming, 119:331–352, 2009.
P. Bonami and J.P.M. Goncalves, 2008. Primal heuristics for mixed integer nonlinear programs. Technical report, IBM Research Report RC24639.
R. Breu and C.-A. Burdet, 19974. “Branch–and–bound experiments in 0–1 programming”, Mathematical Programming Study 2, 1–50.
R. Fourer, D.M. Gay, and B.W. Kernighan, 2003. AMPL: A Modeling Language for Mathematical Programming, Duxbury Press, Brooks/Cole-Thomson Publishing Company, Pacific Grove, CA.
R. Karuppiah 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, 41:163–186.
Roger Fletcher and Sven Leyffer, 1994. Solving Mixed Integer Nonlinear Programming by Outer Approximation, Mathematical Programming, Vol.
66: 327.
R.S. Garfinkel and G.L. Nemhauser, 19972. Integer Programming (John Wiley, New York, 1972).
S. Burer, A. N. Letchford, 2012. Non Covex Mixed-Integer Nonlinear Programming; A Survey, Surves in Operation Research and Management Science 17, 97-106.
S. Lee, I.E. Grosmann, 2001. A global optimization algorithm for non-convex generalized disjunctive programming and applications to process systems.
Comput. Chem. Eng. 25, 1675-1697.
S. Leyffer, 2003. MacMINLP: Test Problems for Mixed Integer Nonlinear Programming, [www http://www-unix.mcs.anl.gov/˜leyffer/MacMINLP].
Tamara G. Kolda, Robert M. Lewis, Virginia Torezon, 2003. Optimization by Direct Search: New Perspective on Some Classical and Modern Methods.
SIAM Review, vol. 45 (1) pp. 385-482.
T. Berthold and A. Gleixner, 2010. Undercover-Primal MINLP Heuristic. In P.
Bonami, L. Liberti, A. Miller and A. Sartenaer (eds). Proceedings of the European Workshop on MINLP, Marseille, pp 103-113.
T. Westerlund and F. Petersson, 1995. A Cutting Plane Method for Solving Convex MINLP Problems, Computers Chem. Eng., vol. 19, pp. 131–136.
T. Westerlund and K. Lundqvist, 2003. Alpha-ECP, Version 5.04. An Interactive MINLP-Solver Based on the Extended Cutting Plane Method, Report 01-178-A.
Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Marti, 2002. A Multistart Scatter Search Heuristic for Smooth NLP and MINLP Problems, INFORMS J. Comput., to appear.