The Mathematical Programming Glossary and Reference Guide

Mathematical programming is a field of mathematics centered on using mathematical models to make decisions. Its goal is to formulate ways to find the best solution to a given problem automatically through optimization. Though mathematical programming depends largely on the accuracy of a model to accomplish its goals, it is vital in helping to break down complex problems and giving decision-makers tools to solve them by selecting the best among many possible alternatives. Mathematical programming benefits from advancements in computer science that allow for the creation of better theoretical models and helps spur those advancements by offering an important perspective for solving problems on the frontiers of computer science research. The links that follow include a variety of quality resources for mathematical programmers.

• What is Mathematical Programming? A definition and basic introduction to the purpose and practice of mathematical programming, including a variety of case studies.
• Mathematical Programming Glossary: Compendium of hundreds of terms relating to mathematical programming.
• Mathematical Programming Society: An international professional society of mathematicians and allies upholding high standards in the practice of mathematical programming and optimization.
• Mathematical Programming Computation: Information on the new scholarly journal sponsored by the Mathematical Programming Society.
• Mathematical Programming: Online access to the Mathematical Programming Society’s more established journal, with free archives dating back to 2008.
• Applied Mathematical Programming: Complete book-length text of this book on mathematical programming from 1977, historically used in Introduction to Optimization courses taught at MIT.
• Operations Research, Mathematical Programming: Introduction, information, and an index of further resources on the relation between operations research and mathematical programming.
• Optimization Online: A moderated depository of high-quality reports on optimization, one of the principal functions of mathematical programming. Offers a monthly digest delivered electronically.
• Mathematical Programming Researchers: Online index of academics who profess mathematical programming as a research interest.
• Mathematical Programming Technical Reports: Archive of reports on mathematical programming in computer science dating back to 1990. Provided by the Optimization Group at the University of Wisconsin (Madison) Department of Computer Sciences.
• Linear / Nonlinear Programming Optimization: Huge index of educational links on the subject of mathematical programming and related disciplines.
• What is Stochastic Programming? Introduction to the stochastic program, a type of mathematical program.
• Mathematical Programming Generator System: Published academic paper available online describing a mathematical program generator.
• Mathematical Programming: Non-commercial resource on the use of SAS/OR software to solve mathematical programming problems.
• Mathematical Programming in Steel Plants: In-depth case study on the use of mathematical programming to optimize tasks in the production of steel.
• Society for Industrial and Applied Mathematics: An interdisciplinary organization promoting cooperation between the mathematical disciplines and the worlds of science and technology which they serve. Includes news and information much of which focuses on the latest industrial uses of mathematical programming and optimization.
• Australian Journal of Mathematical Analysis and Applications: Information and article archives from the definitive Australian scholarly journal of mathematical analysis and programming.
• International Journal of Mathematical Analysis: Website includes online editions of this peer-reviewed research journal dating back to 2008.
• Banach Journal of Mathematical Analysis: Described as “an international open access electronic journal.” Articles freely available online.
• Communications in Mathematical Analysis: Information and archives of this biannual research journal.
• Journal of Contemporary Mathematical Analysis: Information and online access to the complete material of the most recent volumes of the journal by the Armenian Academy of Sciences.
• Bulletin of Mathematical Analysis and Applications: Biannual journal focusing on abstract and applied mathematical analysis.
• Computational Problems and Mathematical Programming: Summary explanation of the relationship between computational problems and mathematical programming. Several examples and diagrams.
• Nurse Scheduling Using Mathematical Programming: Case study from the Journal of Operations Research. Text freely available. Main website includes archives of the Journal from 1992 to 2009.
• Two Mathematical Programming Models of Cheese Manufacture: A scholarly article from the Journal of Dairy Science discussing standardization issues faced by cheese manufacturers and the use of mathematical programming in solving typical problems.
• Mathematical Programming Formulations for the Examinations Timetable Problem: Another cogent applied example from the African Journal of Science and Technology. Pertains to the prevention of scheduling conflicts in the creation of timetables for university examinations.
• Free Graduate Level Mathematical Programming Course by MIT: Complete study guide and other course material for Introduction to Mathematical Programming as taught by Professor John Tsitsiklis at MIT. All material available as a single download.
• Linear Programming and Optimization Resources: Index of Internet sites offering information, tools, and software used in mathematical programming.
• Math Forum: Game Theory / Linear / Non-Linear: Index of resources for mathematical programming and related fields.
• Math Library: Nonlinear Programming: Similar, but more extensive page of additional resources for mathematical programmers.
• Mathematical Programming in Structural Design: Online access to scholarly article from the American Society of Civil Engineers describing a “generalized formula” for implementing mathematical programming in structural design.
• Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling: Abstract and online access to this report from the Air Force Institute of Technology on the use of mathematical programming in the U.S. Air Force.
• What is Logistics Operation Analysis?: Overview of logistics operation analysis in the military and the role of mathematical programming and modeling. From the U.S. Marine Corps.