Nathan Grieve, An Introduction to Mathematical Programming and Network Science: Examples with Theory and Python

This text provides a practical, hands-on introduction to the fundamental concepts of mathematical programming and network science. Particular emphasis is placed on linear programming, mathematical modelling and case studies, the implementation of the Simplex Method in Python, and classical techniques from nonlinear convex programming. The text also features a discussion of mathematical programming within the context of algebraic modelling languages. Further, it includes material on matrix games, decision analysis, multicriteria optimization and non-directed networks. Designed as an introductory resource for upper-level undergraduate and graduate students, the book assumes only a modest mathematical background. Readers who have completed a second course in linear algebra, multivariable calculus, and an introductory course in probability and statistics will find the more advanced portions of the text especially accessible. Researchers and professionals in mathematics, engineering, technology, economics, business, and other quantitatively oriented fields will also find this book a valuable reference. First time readers may very well wish to omit entirely the technical details of the Simplex Method. Instead, they may prefer to immediately turn to the linear programming features of the Python package ize and/or other linear programming solving platforms. This is a perfectly fine way to proceed. All of the mathematical programs that appear in the examples and exercises that are contained in this text can be solved using the features of the Python packages numpy, mathplotlib and scipy. We also illustrate how to solve such programming problems using the most basic features of the Algebraic Modelling Language Pyomo. (See Chapters 6 and 11 for further details.) Readers with background and interest in computer programming are encouraged to give their own direct implementation of the Simplex Method in computer programming languages such as Python, C++ or Java. With this in mind, our presentation here of the Simplex Method, via the theory of Tucker Tableau, allows for an efficient and direct implementation in any of these programming languages. This is illustrated in Chapter 6 which includes a pragmatic implementation of Tucker Tableau and the Simplex Method within Python. Introduction Linear Programming Models—A Collection of Case Study Type Towards a Theory for Mathematical Programming Problems Using Computer Software to Solve Selected Nonlinear Programming Problems. Introduction to Game Theory, Decision Analysis and Multicriteria Optimization