Chapman and Hall/CRC
413 pages | 50 B/W Illus.
Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications
Supplies enough mathematical rigor yet accessible enough for undergraduates
Integrating a hands-on learning approach, a strong linear algebra focus, Maple™ software, and real-world applications, Linear and Nonlinear Programming with Maple™: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming.
Essential linear algebra tools
Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms.
Maple enhances conceptual understanding and helps tackle problems
Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized real-world applications.
Hands-on activities that engage students
Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.
"… this text could be ideal for the right course and the right group of students. An independent or directed study in mathematical programming using this book could be an excellent introduction to applied optimization for an interested group of undergraduates. …"
—MAA Reviews, March 2010
An Introduction to Linear Programming
The Basic Linear Programming Problem Formulation
Linear Programming: A Graphical Perspective in R2
Basic Feasible Solutions
The Simplex Algorithm
The Simplex Algorithm
Alternative Optimal/Unbounded Solutions and Degeneracy
Excess and Artificial Variables: The Big M Method
A Partitioned Matrix View of the Simplex Method
The Revised Simplex Algorithm
Moving beyond the Simplex Method: An Interior Point Algorithm
Standard Applications of Linear Programming
The Diet Problem
Transportation and Transshipment Problems
Basic Network Models
Duality and Sensitivity Analysis
The Dual Simplex Method
Integer Linear Programming
An Introduction to Integer Linear Programming and the Branch and Bound Method
The Cutting Plane Algorithm
Algebraic Methods for Unconstrained Problems
Nonlinear Programming: An Overview
Differentiability and a Necessary First-Order Condition
Convexity and a Sufficient First-Order Condition
Sufficient Conditions for Local and Global Optimal Solutions
Numeric Tools for Unconstrained Nonlinear Problems
The Steepest Descent Method
The Levenberg–Marquardt Algorithm
Methods for Constrained Nonlinear Problems
The Lagrangian Function and Lagrange Multipliers
Convex Nonlinear Problems
Saddle Point Criteria
Sequential Quadratic Programming
Appendix A: Projects
Appendix B: Important Results from Linear Algebra
Appendix C: Getting Started with Maple
Appendix D: Summary of Maple Commands
Exercises appear at the end each section.