I Theoretical and Practical Concepts of Modeling Languages.- 1 Mathematical Optimization and the Role of Modeling Languages.- 2 Models and the History of Modeling.- 3 Mathematical Model Building.- 4 Theoretical Concepts and Design of Modeling Languages.- 5 The Importance of Modeling Languages for Solving Real-World Problems.- II The Modeling Languages in Detail.- 6 The Modeling Language AIMMS.- 7 Design Principles and New Developments in the AMPL Modeling Language.- 8 General Algebraic Modeling System (GAMS).- 9 The LINGO Algebraic Modeling Language.- 10 The LPL Modeling Language.- 11 The MINOPT Modeling Language.- 12 Mosel: A Modular Environment for Modeling and Solving Optimization Problems.- 13 The MPL Modeling System.- 14 The Optimization Systems MPSX and OSL.- 15 The NOP-2 Modeling Language.- 16 The OMNI Modeling System.- 17 The OPL Studio Modeling System.- 18 PCOMP: A Modeling Language for Nonlinear Programs with Automatic Differentiation.- 19 The Tomlab Optimization Environment.- III The Future of Modeling Systems.- 20 The Future of Modeling Languages and Modeling Systems.- References.
