Cutting Plane Algorithm for Convex Generalized Disjunctive Programs

Published Online:https://doi.org/10.1287/ijoc.2015.0669

References

  • Abhishek K, Leyffer S, Linderoth J (2010) FilMINT: An outer approximation-based solver for convex mixed-integer nonlinear programs. INFORMS J. Comput. 22:555–567.LinkGoogle Scholar
  • Balas E (1985) Disjunctive programming and a hierarchy of relaxations for discrete continuous optimization problems. SIAM. J. Algebraic Discrete Methods 6:466–486.CrossrefGoogle Scholar
  • Belotti P, Kirches C, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numerica 22:1–131.CrossrefGoogle Scholar
  • Biegler LT, Grossmann IE, Westerberg AW (1997) Systematic Methods of Chemical Process Design, Prentice Hall International Series in the Physical and Chemical Engineering Sciences (Prentice Hall PTR, Upper Saddle River, NJ).Google Scholar
  • Bonami P, Kilinç M, Linderoth J (2012) Algorithms and software for convex mixed integer nonlinear programs. Lee J, Leyffer S, eds. Mixed Integer Nonlinear Programming (Springer, New York), 1–39.CrossrefGoogle Scholar
  • Brooke A, Kendrick D, Meeraus A, Raman R (1998) GAMS: A users’ guide, GAMS Development Corporation, Washington, DC.Google Scholar
  • Ceria S, Soares J (1999) Convex programming for disjunctive convex optimization. Math. Programming 86:595–614.CrossrefGoogle Scholar
  • Clocksin WF, Mellish CS (1981) Programming in Prolog (Springer-Verlag, Berlin).Google Scholar
  • Dakin RJ (1965) A tree-search algorithm for mixed programming problems. Comput. J. 8:250–255.CrossrefGoogle Scholar
  • Duran M, Grossmann IE (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Programming 36:307–339.CrossrefGoogle Scholar
  • Fletcher R, Leyffer S (1994) Solving mixed integer nonlinear programs by outer approximation. Math. Programming 66:327–349.CrossrefGoogle Scholar
  • Floudas CA (1995) Nonlinear and Mixed Integer Optimization: Fundamentals and Applications (Oxford University Press, Oxford, UK).CrossrefGoogle Scholar
  • Geoffrion AM (1972) Generalized benders decomposition. J. Optim. Theory Appl. 10:237–260.CrossrefGoogle Scholar
  • Grossmann IE (2002) Review of nonlinear mixed-integer and disjunctive programming techniques. Optim. Engrg. 3:227–252.CrossrefGoogle Scholar
  • Grossmann IE, Lee S (2003) Generalized convex disjunctive programming: Nonlinear convex hull relaxation. Comput. Optim. Appl. 26:83–100.CrossrefGoogle Scholar
  • Grossmann IE, Trespalacios F (2013) Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming. AIChE J. 59(9):3276–3295.CrossrefGoogle Scholar
  • Gupta OK, Ravindran A (1985) Branch and bound experiments in convex nonlinear integer programming. Management Sci. 31:1533–1546.LinkGoogle Scholar
  • Lee S, Grossmann IE (2000) New algorithms for nonlinear generalized disjunctive programming. Comput. Chemical Engrg. 24:2125–2141.CrossrefGoogle Scholar
  • Lee S, Grossmann IE (2005) Logic-based modeling and solution of nonlinear discrete/continuous optimization problems. Ann. Oper. Res. 139(1):267–288.CrossrefGoogle Scholar
  • Nemhauser GL, Wolsey LA (1988) Integer and Combinatorial Optimization (Wiley-Interscience, New York).CrossrefGoogle Scholar
  • Quesada I, Grossmann IE (1992) An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Comput. Chemical Engrg. 16:937–947.CrossrefGoogle Scholar
  • Raman R, Grossmann IE (1994) Modeling and computational techniques for logic-based integer programming. Comput. Chemical Engrg. 18:563–578.CrossrefGoogle Scholar
  • Ruiz JP, Grossmann IE (2012) A hierarchy of relaxations for nonlinear convex generalized disjunctive programming. Eur. J. Oper. Res. 218:38–47.CrossrefGoogle Scholar
  • Sawaya N (2006) Reformulations, relaxations and cutting planes for generalized disjunctive programming. Ph.D. thesis, Carnegie Mellon University, Pittsburgh.Google Scholar
  • Sawaya N, Grossmann IE (2012) A hierarchy of relaxations for linear generalized disjunctive programming. Eur. J. Oper. Res. 216:70–82.CrossrefGoogle Scholar
  • Sawaya NW, Grossmann IE (2005) A cutting plane method for solving linear generalized disjunctive programming problems. Comput. Chemical Engrg. 29:1891–1913.CrossrefGoogle Scholar
  • Stubbs R, Mehrotra S (1999) A branch-and-cut method for 0-1 mixed convex programming. Math. Programming 86:515–532.CrossrefGoogle Scholar
  • Trespalacios F, Grossmann IE (2014a) Algorithmic approach for improved mixed-integer reformulations of convex generalized disjunctive programs. INFORMS J. Comput. 27:59–74.LinkGoogle Scholar
  • Trespalacios F, Grossmann IE (2014b) Review of mixed-integer nonlinear and generalized disjunctive programming applications in process systems engineering. SIAM. Forthcoming.Google Scholar
  • Trespalacios F, Grossmann IE (2014c) Review of mixed-integer nonlinear and generalized disjunctive programming methods. Chemie Ingenieur Technik 86(7):991–1012.CrossrefGoogle Scholar
  • Turkay M, Grossmann IE (1996) A logic-based outer-approximation algorithm for MINLP optimization of process flowsheets. Comput. Chemical Engrg. 20:959–978.CrossrefGoogle Scholar
  • Vecchietti A, Lee S, Grossmann IE (2003) Modeling of discrete/continuous optimization problems: Characterization and formulation of disjunctions and their relaxations. Comput. Chemical Engrg. 27:433–448.CrossrefGoogle Scholar
  • Westerlund T, Pettersson F (1995) An extended cutting plane method for solving convex MINLP problems. Comput. Chemical Engrg. 19:131–136.CrossrefGoogle Scholar
  • Williams HP (1985) Model Building in Mathematical Programming (Wiley, New York).Google Scholar
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