zbMATH — the first resource for mathematics

Interactions between nonlinear programming and modeling systems. (English) Zbl 0887.90155
Summary: Modeling systems are very important for bringing mathematical programming software to nonexpert users, but few nonlinear programming algorithms are today linked to a modeling system. The paper discussed the advantages of linking modeling systems with nonlinear programming. Traditional algorithms can be linked using black-box function and derivatives evaluation routines for local optimization. Methods for generating this information are discussed. More sophisticated algorithms can get access to almost any type of information: interval evaluations and constraint restructuring for detailed preprocessing, second order information for sequential quadratic programming and interior point methods, and monotonicity and convex relaxations for global optimization. Some of the sophisticated information is available today; the rest can be generated on demand.
Reviewer: Reviewer (Berlin)

90C30 Nonlinear programming
68Q45 Formal languages and automata
Full Text: DOI
[1] E.D. Andersen and K.D. Andersen, Presolving in linear programming,Mathematical Programming 71 (1995) 221–245. · Zbl 0846.90068
[2] E.D. Andersen and Y. Ye, A computational study of the homogeneous algorithm for large-scale convex optimization, Tech. Rept. no. 3/1996, Dept. of Management, Odense University, Denmark, 1996. · Zbl 0914.90212
[3] M. Berz, C. Bischof, C. Corliss and A. Griewank,Computational Differentiation, Techniques, Applications and Tools (SIAM, Philadelphia, PA, 1996). · Zbl 0857.00033
[4] L. de Bever, ed.,TSP at University of Wisconsin (Manual from the Computing Center, University of Wisconsin, 1977).
[5] C.H. Bischof, A. Carle, P.M. Khademi, A. Mauer and P. Hovland, The ADAFOR 2.0 user’s guide, Tech. Memorandum ANL/MCS-TM-192, Mathematics and Computer Science Division, Argonne National Laboratory, 1994.
[6] J. Bisschop and A. Meeraus, On the development of a general algebraic modeling system in a strategic planning environment,Mathematical Programming Study 20 (1982) 1–29. · doi:10.1007/BFb0121223
[7] J. Bisschop and R. Entriken,AIMMS – The Modeling System (Paragon Decision Technology, Haarlem, The Netherlands, 1993).
[8] A.L. Brearley, G. Mitra and H.P. Williams, Analysis of Mathematical programming problems prior to applying the Simplex method,Mathematical Programming 8 (1975) 54–83. · Zbl 0317.90037 · doi:10.1007/BF01580428
[9] A. Brooke, D. Kendrick and A. Meeraus,GAMS – A User’s Guide (The Scientific Press, Redwood City, CA 1988).
[10] A. Brooke, A. Drud and A. Meeraus, High level modeling systems and nonlinear programming, in:, P.T. Boggs, R.H. Byrd and R.B. Schnabel, eds.,Numerical Optimization 1984 (SIAM, Philadelphia, PA, 1985). · Zbl 0556.65052
[11] J.W. Chinneck and E.W. Dravnieks, Locating minimal infeasible constraint sets in linear programs,ORSA Journal on Computing 3 (1991) 157–168. · Zbl 0755.90055 · doi:10.1287/ijoc.3.2.157
[12] A.R. Conn, N.I.M. Gould and P.L. Toint,LANCELOT, a Fortran package for large-scale nonlinear optimization (Release A), Computational Mathematics, Vol. 17 (Springer, Berlin, 1992). · Zbl 0761.90087
[13] S.P. Dirkse and M.C. Ferris, The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems,Optimization Methods and Software 5 (1995) 123–156. · doi:10.1080/10556789508805606
[14] A. Drud, Interfacing modeling systems and solution algorithms,Journal of Economic Dynamics and Control 5 (1983) 131–149.
[15] A.S. Drud, CONOPT – A large scale GRG code,ORSA Journal on Computing 6 (1994) 207–216. · Zbl 0806.90113 · doi:10.1287/ijoc.6.2.207
[16] A.S. Drud,CONOPT – A System for Large Scale Nonlinear Optimization, REFERENCE MANUAL for CONOPT Subroutine Library (ARKI Consulting and Development A/S, Bagsvaerd, Denmark, 1996).
[17] M.A. Duran and I.E. Grossmann, An outer-approximation algorithm for a class of mixed-integer nonlinear programs,Mathematical Programming 36 (1986) 307–339. · Zbl 0619.90052 · doi:10.1007/BF02592064
[18] R. Fourer, D.M. Gay and B.W. Kernighan,AMPL – A Modeling Language for Mathematical Programming (The Scientific Press, Redwood City, CA, 1993). · Zbl 0701.90062
[19] R. Fourer, Modeling languages versus matrix generators for linear programming,ACM Transactions on Mathematical Software 9 (1983) 143–183. · doi:10.1145/357456.357457
[20] GAMS – The Solver Manuals (GAMS Development Corporation, Washington, DC, 1996).
[21] D.M. Gay, More AD of Nonlinear AMPL Models: Computing Hessian Information and Exploiting Partial Separability, in: M. Berz, C. Bischof, C. Corliss and A. Griewank,Computational Differentiation, Techniquès, Applications and Tools (SIAM, Philadelphia, PA, 1996). · Zbl 0866.65018
[22] P.E. Gill, W. Murray, M.A. Saunders and M.H. Wright, User’s guide for NPSOL (Version 4.0): A Fortran package for nonlinear programming, Tech. Rept. SOL 86-2, Dept. of Operations Research, Stanford University, 1986.
[23] A. Griewank and G.F. Corliss, eds.,Automatic Differentiation of Algorithms: Theory, Implementation, and Application (SIAM, Philadelphia, PA, 1992).
[24] A. Griewank, D. Juedes and J. Utke, Algorithm 755: ADOL-C: A package for the automatic differentiation of algorithms written in C/C++,ACM Transactions on Mathematical Software 22 (1996) 131–167. · Zbl 0884.65015 · doi:10.1145/229473.229474
[25] L.S. Lasdon, A.D. Waren, A. Jain and M. Ratner, Design and testing of a generalized gradient code for nonlinear programming,ACM Transactions on Mathematical Software 4 (1978) 34–50. · Zbl 0378.90080 · doi:10.1145/355769.355773
[26] LINGO – The Modeling Language and Optimizer (LINDO Systems Inc., Chicago, IL, 1995).
[27] I.J. Lustig, R.E. Marsten and D.F. Shanno, Interior point methods for linear programming: Computational state of the art,ORSA Journal on Computing 6 (1994) 1–14. · Zbl 0798.90100 · doi:10.1287/ijoc.6.1.1
[28] G.P. McCormick, Computability of global solutions to factorable nonconvex programs: Part I – Convex underestimating problems,Mathematical Programming 10 (1976) 147–175. · Zbl 0349.90100 · doi:10.1007/BF01580665
[29] R. Moore,Interval Analysis (Prentice Hall, Englewood Cliffs, NJ, 1966). · Zbl 0176.13301
[30] B.A. Murtagh and M.A. Saunders, A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,Mathematical Programming Study 16 (1982) 84–117. · Zbl 0477.90069 · doi:10.1007/BFb0120949
[31] P.C. Piela, T.G. Epperly, K.M. Westerberg and A.W. Westerberg, ASCEND: An object-oriented computer environment for modeling and analysis: The modeling language,Computers and Chemical Engineering 15 (1991) 53–72. · doi:10.1016/0098-1354(91)87006-U
[32] H.S. Ryoo and N.V. Sahinidis, A branch-and-reduce approach to global optimization,Journal of Global Optimization 8 (1996) 107–139. · Zbl 0856.90103 · doi:10.1007/BF00138689
[33] N.V. Sahinidis, BARON: A general purpose global optimization software package,Journal of Global Optimization 8 (1996) 201–205. · Zbl 0856.90104 · doi:10.1007/BF00138693
[34] J. Viswanathan and I.E. Grossman, A combined penalty function and outer approximation method for MINLP optimization,Computers and Chemical Engineering 14 (1990) 769–782. · doi:10.1016/0098-1354(90)87085-4
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.