عنوان

Mathematics of optimization :

1470441144

9781470441142

Mathematics of optimization :

[Book]

how to do things faster /

Steven J. Miller.

Providence, Rhode Island :

American Mathematical Society,

[2017]

©2017

xxii, 327 pages :

illustrations (some color) ;

27 cm

Pure and Applied Undergraduate Texts ;

The Sally series

30

Includes bibliographical references (pages 317-321) and index.

Part 1 . Classical Algorithms -- Chapter 1. Efficient Multiplication, I -- Chapter 2. Efficient Multiplication, II -- Part 2 . Introduction to Linear Programming -- 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 -- Part 3 . Advanced Linear Programming -- 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 -- Part 4 . Fixed Point Theorems -- 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 19. The Four Color Problem -- Chapter 20. The Kepler Conjecture

0

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--back cover.

Management science, Problems, exercises, etc.

Mathematical optimization, Problems, exercises, etc.

Operations research, Problems, exercises, etc.

Computer science-- Theory of computing-- Analysis of algorithms and problem complexity.

Functional analysis-- Miscellaneous applications of functional analysis-- Applications in optimization, convex analysis, mathematical programming, economics.

Global analysis, analysis on manifolds-- Calculus on manifolds; nonlinear operators-- Fixed point theorems on manifolds.

Management science.

Mathematical optimization.

Mathematics education-- Mathematical modeling, applications of mathematics-- Operations research, economics.

Number theory-- Computational number theory-- Algorithms; complexity.

Numerical analysis-- Mathematical programming, optimization and variational techniques-- Optimization and variational techniques.

Operations research, mathematical programming-- Mathematical programming-- Linear programming.

Operations research.

Miller, Steven J.,1974-

20200823025818.0

rda

[Book]

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