Papers on Mathematical Modeling


A. Neumaier, Mathematical Model Building, Chapter 3 in: Modeling Languages in Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003. (pdf) Some notes on mathematical modeling, listing motivations, applications, a numerical toolkit, general modeling rules, modeling conflicts, useful attitudes, and structuring the modeling work into 16 related activities by means of a novel modeling diagram.

A. Neumaier, Fuzzy modeling in terms of surprise, Fuzzy Sets and Systems 135 (2003), 21-38.

A. Neumaier, Molecular Modeling of Proteins and Mathematical Prediction of Protein Structure, SIAM Review 39 (1997), 407-460.

H. Schichl, Models and the History of Modeling, Chapter 2 in: Modeling Languages in Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003.(pdf) After a very fast tour through 30,000 years of modeling history, the basic ingredients to models in general, and to mathematical models in particular, are described.

H. Schichl, Theoretical Concepts and Design of Modeling Languages, Chapter 4 in: Modeling Languages in Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003.(pdf) The basic design features of modeling languages and particularly algebraic modeling languages are presented. An important class of optimization problems --- global optimization is introduced, and the difficulties in constructing models for such problems are illustrated.

H. Schichl and A. Neumaier, The NOP-2 Modeling Languages, Chapter 15 in: Modeling Languages in Mathematical Optimization (J. Kallrath, ed.), Kluwer, Boston 2003.(pdf) A short overview over the modeling language NOP-2 for specifying general optimization problems, including constrained local or global nonlinear programs and constrained single and multistage stochastic programs, is presented. The proposed language is specifically designed to represent the internal (separable and repetitive) structure of the problem.

H. Schichl, A. Neumaier and S. Dallwig, The NOP-2 modeling language, Ann. Oper. Research 104 (2001), 281-312. (pdf) An enhanced version NOP-2 of the NOP language for specifying global optimization problems is described. Because of its additional features, NOP-2 is comparable to other modeling languages like AMPL and GAMS, and allows the user to define a wide range of problems arising in real life applications such as global constrained (and even stochastic) optimization programs. NOP-2 permits named variables, parameters, indexing, loops, relational operators, extensive set operations, matrices and tensors, and parameter arithmetic. The main advantage that makes NOP-2 look and feel considerably different from other modeling languages is the display of the internal analytic structure of the problem. It is fully flexible for interfacing with solvers requiring special features such as automatic differentiation or interval arithmetic.

Josef Kallrath; Introduction: Models, Model Building, and Mathematical Optimization - The Importance of Modeling Languages for Solving Real-World Problems

Hermann Schichl; Modeling Languages and Global Optimization

Jan Bisschop; AIMMS - An All-Round Development Environment

Collective Communication Optimization with Dynamic Programming in Heterogeneous Cluster Environments

Modeling Systems Preview

Spreadsheets

Modeling Environments

Papers (EconPapers)

Geoffrion, A.M., "Structured Modeling," in Encyclopedia of Operations Research & Management Science, S.I. Gass and C.M. Harris (Eds.), Kluwer Academic Publishers (1996). Revised version published in the Centennial Edition, 2001.

Geoffrion, A.M., "An Introduction to Structured Modeling," Management Science, 33:5, 547-588 (May 1987).

Geoffrion, A.M., "An Introduction to Structured Modeling," Management Science, 33:5, 547-588 (May 1987).

Geoffrion, A.M., "The Formal Aspects of Structured Modeling," Operations Research, 37:1, 30-51 (January-February 1989).

Geoffrion, A.M., "Computer-Based Modeling Environments," European Journal of Operational Research, 41:1, 33-43 (July 1989).

Geoffrion, A.M., "FW/SM: A Prototype Structured Modeling Environment," Management Science, 37:12, 1513-1538 (December 1991).

Geoffrion, A.M., "The SML Language for Structured Modeling: Levels 1 and 2," Operations Research, 40:1, 38-57 (January-February 1992).

Geoffrion, A.M., "The SML Language for Structured Modeling: Levels 3 and 4," Operations Research, 40:1, 58-75 (January-February 1992).

Geoffrion, A.M., "Indexing in Modeling Languages for Mathematical Programming," Management Science, 38:3, 325-344 (March 1992).

Geoffrion, A.M., "Structured Modeling: Survey and Future Research Directions," ORSA CSTS Newsletter, 15:1, 11 pages (Spring, 1994). Updated May, 1996 and June, 1999 and published in ITORMS: Interactive Transactions on Operations Research and Management Science, 1:3.

Geoffrion, A.M., "An Informal Annotated Bibliography on Structured Modeling," ITORMS: Interactive Transactions on Operations Research and Management Science, 1:2Most recently updated June, 1999.