# Optimization

### What is Mathematical Programming

- from George B. Dantzig, Father of Mathematical Programming, "The Nature of Mathematical Programming"

Mathematical programming is the study or use of the mathematical program. It includes any or all of the following:

- Theorems about the form of a solution, including whether one exists;
- Algorithms to seek a solution or ascertain that none exists;
- Formulation of problems into mathematical programs, including understanding the quality of one formulation in comparison with another;
- Analysis of results, including debugging situations, such as infeasible or anomalous values;
- Theorems about the model structure, including properties pertaining to feasibility, redundancy and/or implied relations (such theorems could be to support analysis of results or design of algorithms);
- Theorems about approximation arising from imperfections of model forms, levels of aggregation, computational error, and other deviations;
- Developments in connection with other disciplines, such as a computing environment.