Linear Programming and Generalizations A Problem-based Introduction with Spreadsheets - Denardo, Eric V.; SpringerLink (Boston, MA Springer US Imprint: Springer, 2011)
This book on constrained optimization is novel in that it fuses these themes: use examples to introduce general ideas; engage the student in spreadsheet computation; survey the uses of constrained optimization;. investigate game theory and nonlinear optimization, link the subject to economic reasoning, and present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the students interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the students grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.
Chapter 1. Introduction to Linear Programs -- Chapter 2. Spreadsheet Computation -- Chapter 3. Mathematical Preliminaries -- Chapter 4. The Simplex Method, Part 1 -- Chapter 5. Analyzing Linear Programs -- Chapter 6. The Simplex Method, Part 2 -- Chapter 7. A Survey of Optimization Problems -- Chapter 8. Path-Length Problems and Dynamic Programming -- Chapter 9. Flows in Networks -- Chapter 10. Vector Spaces and Linear Programs -- Chapter 11. Multipliers and the Simplex Method -- Chapter 12. Duality -- Chapter 13. The Dual Simplex Pivot and Its Uses -- Chapter 14. Introduction to Game Theory -- Chapter 15. The Bi-Matrix Game -- Chapter 16. Fixed Points and Equilibria -- Chapter 17. Convex Sets -- Chapter 18. Differentiation -- Chapter 19. Convex Functions -- Chapter 20 -- Nonlinear Programs.
Electronic reproduction.
Keywords: Linear programming; Electronic books