Mathematics of optimization : how to do things faster

著者

• Miller, Steven J.

書誌事項

Mathematics of optimization : how to do things faster

Steven J. Miller

（The Sally series, . Pure and applied undergraduate texts ; 30）

American Mathematical Society, c2017

注記

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

内容説明・目次

内容説明

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.

目次

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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB25285397
• ISBN:
  • 9781470441142
• LCCN: 2017029521
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: xxii, 327 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA402.5
  • DC23 : 519.6
• 件名:
  • LCSH : Mathematical optimization -- Problems, exercises, etc
  • LCSH : Operations research -- Problems, exercises, etc
  • LCSH : Management science -- Problems, exercises, etc
• 親書誌ID:
  • BA8980131X