AMPL

AMPL, short for A Mathematical Programming Language, is a high-level modeling language for mathematical optimization. It provides a declarative approach that allows users to describe objectives, variables, and constraints in a way that mirrors mathematical notation, while keeping the data separate from the model. A model is built from sets, parameters, variables, and equations; indexing and algebraic expressions enable compact formulations of large problems. AMPL itself does not solve problems—it translates models into input for external optimization solvers and manages data input and result retrieval.

AMPL was developed in the 1980s by Robert Fourer, David M. Gay, and Brian D. Kernighan. Since its introduction, it has become a widely used tool in academia and industry for linear, nonlinear, and mixed-integer programs, as well as some stochastic and nonconvex formulations.

Usage typically involves writing a model file with the .mod extension and a data file with the .dat extension (or providing data inline). The user loads both into an AMPL session, selects a solver with the option solver directive, and issues solve. AMPL then communicates with the solver, returning optimal values for the decision variables and other derived quantities. The language is solver-agnostic; it supports a range of commercial and open-source solvers, such as CPLEX, Gurobi, Xpress, KNITRO, IPOPT, CBC, and GLPK. For solvers that use their own native formats, AMPL can generate solver-specific input or an intermediate NL representation.

AMPL is widely used for applications in operations research, including production planning, scheduling, network design, energy systems, and logistics. Its separation of model and data, rich algebraic syntax, and extensible solver interface contribute to its persistence in teaching and professional modeling.