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.
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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.
Bentley, J.L. (Aug. 1986), “Little Languages,” Communications oJ the ACM 29 #8: 711–721.
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.
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.
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.
Fourer, R. (1983), “Modeling Languages Versus Matrix Generators for Linear Programming,” ACM Trans. Math. Software 9 #2: 143–183.
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.
Gay, D.M. (1985), “Electronic Mail Distribution of Linear Programming Test Problems,” COALNewsletter#13: 10–12.
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.
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).
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).
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.
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).
Griewank, A. and Toint, Ph.L. (1984), “On the Existence of Convex Decompositions of Partially Separable Functions,” Math. Programming 28: 25–49.
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.
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Gay, D.M. (2001). Symbolic-Algebraic Computations in a Modeling Language for Mathematical Programming. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_10
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_10
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