# Symbolic-Algebraic Computations in a Modeling Language for Mathematical Programming

Conference paper

## Abstract

AMPL is a language and environment for expressing and manipulating *mathematical programming* problems, i.e., minimizing or maximizing an algebraic objective function subject to algebraic constraints. The AMPL processor simplifies problems, as discussed in more detail below, but calls on separate *solvers* to actually solve problems. Sol vers obtain information ab out the problems they solve, including first and, for some solvers, second derivatives, from the AMPL/solver interface library.

## Keywords

Variable Bound Mathematical Programming Problem Automatic Differentiation Separable Structure Expression Graph
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## References

*IEEE StandardJor Binary Floating-Point Arithmetic*, Institute of Electrical and Electronics Engineers, New York, NY, 1985. ANSI/IEEE Std 754–1985.Google Scholar- Bentley, J.L. (Aug. 1986), “Little Languages,”
*Communications oJ the ACM***29**#8: 711–721.MathSciNetCrossRefGoogle Scholar - Conn, A.R.; Gould, N.I.M.; and Toint, Ph.L.,
*LANCELOT, a Fortran Package Jor Large-Scale Nonlinear Optimization (Release A)*, Springer-Verlag, 1992. Springer Series in Computational Mathematics 17.Google Scholar - Feldman, S.I.; Gay, D.M.; Maimone, M.W.; and Schryer, N.L., “A Fortran-to-C Converter,” Computing Science Technical Report No. 149 (1990), Bell Laboratories, Murray Hill, NJ.Google Scholar
- Ferris, Michael C.; Fourer, Robert; and Gay, David M. (1999), “Expressing Complementarity Problems in an Algebraic Modeling Language and Communicating Them to Solvers,”
*SIAM Journal on Optimization***9**#4: 991–1009.MathSciNetMATHCrossRefGoogle Scholar - Fourer, R. (1983), “Modeling Languages Versus Matrix Generators for Linear Programming,”
*ACM Trans. Math. Software***9**#2: 143–183.CrossRefGoogle Scholar - Fourer, Robert; Gay, David M.; and Kemighan, Brian W.,
*AMPL: A Modeling Language for Mathematical Programming*, Duxbury Press/Wadsworth, 1993. ISBN: 0-89426-232-7.Google Scholar - Gay, D.M. (1985), “Electronic Mail Distribution of Linear Programming Test Problems,”
*COALNewsletter*#13: 10–12.Google Scholar - Gay, D.M., “Correctly Rounded Binary-Decimal and Decimal-Binary Conversions,” Numerical Analysis Manuscript 90-10 (11274-901130-10TMS) (1990), Bell Laboratories, Murray Hili, NJ.Google Scholar
- Gay, David M., “Automatic Differentiation of Nonlinear AMPL Models,” pp. 61–73 in
*Automatic Differentiation of Algorithms: Theory, Implementation, and Application*, ed. A. Griewank and G.F. Corliss, SIAM (1991).Google Scholar - Gay, D.M., “More AD of Nonlinear AMPL Models: Computing Hessian Information and Exploiting Partial Separability,” in
*Computational Differentiation: Applications, Techniques, and Tools*, ed. George F. Corliss, SIAM (1996).Google Scholar - Gay, David M., “Hooking Your Solver to AMPL,” Technical Report 97-4-06 (April, 1997), Computing Sciences Research Center, Bell Laboratories. See http://www.ampl.com/ampl/REFS/hooking2.ps.gz.Google Scholar
- Griewank, A. and Toint, Ph.L., “On the Unconstrained Optimization of Partially Separable Functions,” pp. 301–312 in
*Nonlinear Optimization 1981*, ed. M. J. D. Powell, Academic Press (1982).Google Scholar - Griewank, A. and Toint, Ph.L. (1984), “On the Existence of Convex Decompositions of Partially Separable Functions,”
*Math. Programming***28**: 25–49.MathSciNetMATHCrossRefGoogle Scholar - Murtagh, B.A. and Saunders, M.A. (1982), “A Projected Lagrangian Algorithm and its Implementation for Sparse Nonlinear Constraints,”
*Math. Programming Study***16**: 84–117.MathSciNetMATHCrossRefGoogle Scholar

## Copyright information

© Springer-Verlag Wien 2001