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Full Description
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.
Contents
Classical algorithms: Efficient multiplication, I
Efficient multiplication, II
Introduction to linear programming: Introduction to linear programming
The canonical linear programming problem
Symmetries and dualities
Basic feasible and basic optimal solutions
The simplex method
Advanced linear programming: Integer programming
Integer optimization
Multi-objective and quadratic programming
The traveling salesman problem
Introduction to stochastic linear programming
Fixed point theorems: Introduction to fixed point theorems
Contraction maps
Sperner's lemma
Brouwer's fixed point theorem
Advanced topics: Gale-Shapley algorithm
Interpolating functions
The four color problem
The Kepler conjecture
Index
Bibliography.
