A structure-conveying modelling language for mathematical and stochastic programming

Mathematical Programming Computation

Volumn 1, Issue 4, 2009, Pages 223-247

  Colombo, Marco ^a   Grothey, Andreas ^a   Hogg, Jonathan ^a   Woodsend, Kristian ^a   Gondzio, Jacek ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BLOCK STRUCTURES; CONSTRUCT MODELS; INTERIOR POINT; MODELLING LANGUAGE; NEW APPROACHES; OBJECT-ORIENTED FEATURES; POST PROCESSING; SUBMODELS;

LINEAR ALGEBRA;

STOCHASTIC PROGRAMMING;

EID: 80051682694     PISSN: 18672949     EISSN: 18672957     Source Type: Journal    
DOI: 10.1007/s12532-009-0008-2     Document Type: Article

References (31)

1. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238-252 (1962)
2. Birge, J., Dempster, M., Gassmann, H., Gunn, E., King, A., Wallace, S.: A standard input format for multiperiod stochastic linear programs. Comm. Algorithms Newsl. 17, 1-19 (1987)
3. Bisschop, J., Entriken, R.: AIMMS the modeling system. Paragon Decis. Technol. (1993)
4. Blomvall, J., Lindberg, P.O.: A Riccati-based primal interior point solver for multistage stochastic programming. Eur. J. Oper. Res. 143, 452-461 (2002)
5. Brooke, A., Kendrick, D., Meeraus, A.: GAMS: A User's Guide. The Scientific Press, Redwood City, CA (1992)
6. Buchanan, C., McKinnon, K., Skondras, G.: The recursive definition of stochastic linear programming problems within an algebraic modeling language. Ann. Oper. Res. 104, 15-32 (2001)
7. Colombani, Y., Heipcke, S.: Mosel: an extensible environment for modeling and programming solutions. In: Jussien, N., Laburthe, F. (eds.) Proceedings of the Fourth InternationalWorkshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR '02), pp. 277-290. Le Croisic, France (2002)
8. Dantzig, G.B., Wolfe, P.: The decomposition algorithm for linear programming. Econometrica 29, 767-778 (1961)
9. Ferris, M.C., Horn, D.J.: Partitioning mathematical programs for parallel solution. Math. Programm. 80, 35-62 (1998)
10. Fourer, R.: Proposed new AMPL features: stochastic programming extensions. http://www.ampl.com/ NEW/FUTURE/stoch.html. Accessed 10 February 2009
11. Fourer, R., Gay, D.M.: Conveying problem structure from an algebraic modeling language to optimization algorithms. In: Laguna, M., Velarde, J.G. (eds.) Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, pp. 75-89. Kluwer, Dordrecht (2000)
12. Fourer, R., Lopes, L.: StAMPL: A filtration-oriented modeling tool for stochastic recourse problems. INFORMS Journal on Computing 21, 242-256 (2009)
13. Fourer, R., Gay, D., Kernighan, B.W.: AMPL: A Modeling Language for Mathematical Programming. The Scientific Press, San Francisco, CA (1993)
14. Fragnière, E., Gondzio, J.: Optimization modeling languages. In: Pardalos, P., Resende, M. Handbook of Applied Optimization, pp. 993-1007. Oxford University Press, New York (2002)
15. Fragnière, E., Gondzio, J., Sarkissian, R., Vial, J.-P.: Structure exploiting tool in algebraic modeling languages. Management Science 46, 1145-1158 (2000)
16. Gay, D.M.: Hooking your solver to AMPL, tech. rep., Bell Laboratories, Murray Hill, NJ, (1993) (revised 1994, 1997)
17. Gondzio, J., Grothey, A.: Direct solution of linear systems of size 109 arising in optimization with interior point methods. In: Wyrzykowski, R. Parallel Processing and Applied Mathematics, pp. 513-525. Springer, Berlin vol. 3911 of Lecture Notes in Computer Science (2006)
18. Gondzio, J., Grothey, A.: Parallel interior point solver for structured quadratic programs: Application to financial planning problems. Ann. Oper. Res. 152, 319-339 (2007)
19. Gondzio, J., Grothey, A.: Exploiting structure in parallel implementation of interior point methods for optimization. Comput. Manage. Sci. 6, 135-160 (2009)
20. Gondzio, J., Sarkissian, R.: Parallel interior point solver for structured linear programs. Math. Programm. 96, 561-584 (2003)
21. Grothey, A., Hogg, J., Woodsend, K., Colombo, M., Gondzio, J.: A structure-conveying parallelisable modelling language for mathematical programming. In: Č iegis, R., Henty, D., Kågström, B., Žilinskas, J. (eds.) Parallel Scientific Computing and Optimization: Advances and Applications, pp. 147-158. Springer, Berlin vol. 27 of pringer Optimization and Its Applications (2009)
22. Hochreiter, R.: Simplified stage-based modeling of multi-stage stochastic programming problems. In: Conference Talk: SPXI, Vienna, Austria, August (2007)
23. Kuip, C.A.C.: Algebraic languages for mathematical programming. Eur. J. Oper. Res. 67, 25-51 (1993)
24. Markowitz, H.: Portfolio selection. J. Finance 7(1), 77-91 (1952)
25. Murtagh, B.: Advanced Linear Programming: Computation and Practice. McGraw-Hill, New York (1981)
26. Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) Principles and Practice of Constraint Programming-CP 2000, pp. 369-383. Springer, Berlin/Heidelberg vol. 1894/2000 of Lecture Notes in Computer Science (2000)
27. Sengupta, P.:MILANO, an object-oriented algebraic modeling system. Available from Simulation Sciences Inc. website: http://www.simsci-esscor.com/NR/rdonlyres/C0061CFF-7F7A-4526-8710-D436 2C6DCD36/0/102797.pdf
28. Steinbach, M.: Hierarchical sparsity in multistage convex stochastic programs. In: Uryasev, S., Pardalos, P.M. (eds.) Stochastic Optimization: Algorithms and Applications, pp. 363-388. Kluwer, Dordrecht (2000)
29. Valente, C., Mitra, G., Sadki, M., Fourer, R.: Extending algebraic modelling languages for stochastic programming. INFORMS J. Comput. 21, 107-122 (2009)
30. Van Hentenryck, P.: The OPL Optimization Programming Language. MIT Press, Cambridge (1999)
31. Wallace, S.W., Ziemba, W.T. (eds.): Applications of Stochastic Programming. SIAM, Philadelphia (2005)