## Modeling Languages in Mathematical OptimizationThis book deals with the aspects of modeling and solving real-world optimiza tion problems in a unique combination. It treats systematically the major mod eling languages and modeling systems used to solve mathematical optimization problems. The book is an offspring ofthe 71 st Meeting of the GOR (Gesellschaft fill Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Op timization during April 23-25, 2003 in the German Physics Society Confer ence Building in Bad Honnef, Germany. The modeling language providers AIMMS Johannes Bisschop, Paragon Decision Technology B. V, Haarlem, The Netherlands, AMPL Bob Fourer, Northwestern Univ. ; David M. Gay, AMPL Optimization LLC., NJ, GAMS Alexander Meeraus, GAMS Development Corporation, Washington D.C., Mosel Bob Daniel, Dash Optimization, Blisworth, UK, MPL Bjami Krist jansson, Maximal Software, Arlington, VA, NOP-2 Hermann Schichl, Vienna University, Austria, PCOMP Klaus Schittkowski, Bayreuth University, Germany, and OPL Sofiane Oussedik, ILOG Inc., Paris, France gave deep insight into their motivations and conceptual design features of their software, highlighted their advantages but also critically discussed their limits. The participants benefited greatly from this symposium which gave a useful overview and orientation on today's modeling languages in optimization. Roughly speaking, a modeling language serves the need to pass data and a mathematical model description to a solver in the same way that people, es Of course, in pecially mathematicians describe those problems to each other. |

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agent AIMMS algebraic modeling languages allows AMPL applications array automatic differentiation binary bounds complex components constraint programming cost CPLEX database declarations defined derivatives dynamic end-user equations example expressions forall formulation FORTRAN frac GAMS global optimization implemented infeasible input integer programming interface inventory iterations Jobs keyword linear programming LINGO machine makespan mathematical models mathematical programming MATLAB matrix MILP minimize MINLP MINOPT mixed-integer model developer modeling systems module Mosel MPL Modeling MPSX node nonlinear programming objective function OMNI operations OPL Studio OptiMax optimization models optimization problems option outer approximation param parameters PCOMP period possible programming language provides reactor scheduling search procedure solution algorithm solve solver specified spreadsheet square stochastic structure subroutines syntax Table TOMLAB tool trolley types values vector Visual