LaGO: A (heuristic) Branch and Cut algorithm for nonconvex MINLPs

Central European Journal of Operations Research

Volumn 16, Issue 2, 2008, Pages 127-138

  Nowak, Ivo ^a   Vigerske, Stefan ^b  

^a Deutsche Lufthansa AG   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Branch and bound; Branch and Cut; Global optimization; Mixed integer nonlinear programming; Outer approximation

Indexed keywords

EID: 44349091026     PISSN: 1435246X     EISSN: 16139178     Source Type: Journal    
DOI: 10.1007/s10100-007-0051-x     Document Type: Conference Paper

References (29)

1. Adjiman CS and Floudas CA (1997). Rigorous convex underestimators for general twice-differentiable problems. J Global Optim 9: 23-40
2. Adjiman CS, Dallwig S, Floudas CA and Neumaier A (1998). A global optimization method, αBB, for general twice-differentiable constrained NLPs-I. Theor Adv Comp Chem Eng 22: 1137-1158
3. Adjiman CS, Androulakis IP and Floudas CA (2000). Global optimization of mixed-integer nonlinear problems. AIChE J 46: 1769-1797
4. Ahadi-Oskui T (2006) Optimierung des Entwurfs komplexer Energieumwandlungsanlagen. Fortschritts-Berichte VDI, Reihe 6, Nr. 543. VDI-Verlag
5. Ahadi-Oskui T, Tsatsaronis G (2006) Optimization of the design of a complex energy conversion system using mathematical programming and genetic algorithms. In: Proceedings of IMECE2006
6. Ahadi-Oskui T, Nowak I, Tsatsaronis G, Vigerske S (2007) Optimizing the design of complex energy conversion systems by Branch and Cut. Preprint 07-11. Department of Mathematics, Humboldt University Berlin, http://www.math.hu- berlin.de/publ/pre/2007/P-07-11.pdf (submitted)
7. Akrotirianakis IG and Floudas CA (2004). A new class of improved convex underestimators for twice differentiable constrained NLPs. J Global Optim 30(4): 367-390
8. Bussieck MR, Drud AS and Meeraus A (2003). MINLPLib-a collection of test models for mixed-integer nonlinear programming. INFORMS J Comput 15(1): 114-119
9. Duran MA and Grossmann IE (1986). An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math Prog 36: 307-339
10. Fletcher R and Leyffer S (1994). Solving mixed integer nonlinear programs by outer approximation. Math Program 66(3(A)): 327-349
11. Floudas CA, Akrotirianakis IG, Caratzoulas C, Meyer CA and Kallrath J (2005). Global optimization in the 21st century: advances and challenges. Comput Chem Eng 29(6): 1185-1202
12. GAMS Development Corp. (2003) GAMS-the solver manuals
13. Gonçalves JPM, Ladanyi L (2005) An implementation of a separation procedure for mixed integer rounding inequalities. Research Report RC23686, IBM Research Division, August
14. ILOG, Inc. CPLEX. http://www.ilog.com/products/cple.
15. Lougee-Heimer R (2003) The common optimization interface for operations research. IBM J Res Dev 47(1):57-66. http://www.coin-or.org
16. Marchand H and Wolsey LA (2001). Aggregation and mixed integer rounding to solve MIPs. Oper Res 49(3): 363-371
17. Meyer CA and Floudas CA (2005). Convex underestimation of twice continuously differentiable functions by piecewise quadratic perturbation: Spline αBB. J Global Optim 29(6): 1185-1202
18. Nemhauser GL and Wolsey LA (1988). Integer and combinatorial optimization. Wiley-Interscience, New York
19. Neumaier A (2004) Complete search in continuous global optimization and constraint satisfaction. In: Acta numerica, vol 13, chap 4. Cambridge University Press, Cambridge, pp 271-370
20. Nowak I (1999). A new semidefinite programming bound for indefinite quadratic forms over a simplex. J Global Optim 14(4): 357-364
21. Nowak I (2005a). Lagrangian decomposition of block-separable mixed-integer all-quadratic programs. Math Program 102(2): 295-312
22. Nowak I (2005b). Relaxation and decomposition methods for mixed integer nonlinear programming. Birkhäuser, Basel
23. Nowak I, Alperin H, Vigerske S (2003) LaGO-an object oriented library for solving MINLPs. In: Bliek Ch, Jermann Ch, Neumaier A (eds) Global optimization and constraint satisfaction, volume 2861 of Lecture Notes in Computer Science. Springer, Heidelberg, pp 31-43
24. Nowak I, Vigerske S LaGO-Lagrangian Global Optimizer. https://projects.coin-or.org/LaGO
25. Sahinidis N, Tawarmalani M (2002) BARON. http://archimedes.scs.uiuc.edu/ baron/baron.html
26. Tawarmalani M and Sahinidis NV (2004). Global optimization of mixed-integer nonlinear programs: a theoretical and computational study. Math Program 99: 563-591
27. Tawarmalani M and Sahinidis NV (2002). Convexification and global optimization in continuous and mixed-integer nonlinear programming: theory, algorithms, software and applications. Kluwer, Dordrecht
28. Viswanathan J and Grossmann IE (1990). A combined penalty function and outer-approximation method for MINLP optimization. Comput Chem Eng 14(7): 769-782
29. Wächter A, Biegler LT (2006) On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math Prog 106(1):25-57. http://projects.coin-or.org/Ipopt