(eBook PDF) Mathematics of Optimization: How to Do Things Faster – Digital Ebook – Instant Delivery Download
Product details:
- ISBN-10 : 1470441144
- ISBN-13 : 978-1470441142
- Author: Steven J. Miller
Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the “why” and the “how” in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.
Table contents:
Chapter 1. Efficient Multiplication, I
Chapter 2. Efficient Multiplication, II
Chapter 3. Introduction to Linear Programming
Chapter 4. The Canonical Linear Programming Problem
Chapter 5. Symmetries and Dualities
Chapter 6. Basic Feasible and Basic Optimal Solutions
Chapter 7. The Simplex Method
Chapter 8. Integer Programming
Chapter 9. Integer Optimization
Chapter 10. Multi-Objective and Quadratic Programming
Chapter 11. The Traveling Salesman Problem
Chapter 12. Introduction to Stochastic Linear Programming
Chapter 13. Introduction to Fixed Point Theorems
Chapter 14. Contraction Maps
Chapter 15. Sperner’s Lemma
Chapter 16. Brouwer’s Fixed Point Theorem
Chapter 17. Gale-Shapley Algorithm
Chapter 18. Interpolating Functions
Chapter 19. The Four Color Problem
Chapter 20. The Kepler Conjecture
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