Convexity and its Applications in Discrete and Continuous Optimization
Seiten
2025
Cambridge University Press (Verlag)
978-1-108-83759-0 (ISBN)
Cambridge University Press (Verlag)
978-1-108-83759-0 (ISBN)
This rigorous introduction to the fundamental ideas of convexity and their use in optimization offers a unifying approach for both discrete and continuous applications. Students and researchers in optimization, operations research, computer science, and applied mathematics will appreciate the book's 300+ exercises and coverage of new developments.
Using a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.
Using a pedagogical, unified approach, this book presents both the analytic and combinatorial aspects of convexity and its applications in optimization. On the structural side, this is done via an exposition of classical convex analysis and geometry, along with polyhedral theory and geometry of numbers. On the algorithmic/optimization side, this is done by the first ever exposition of the theory of general mixed-integer convex optimization in a textbook setting. Classical continuous convex optimization and pure integer convex optimization are presented as special cases, without compromising on the depth of either of these areas. For this purpose, several new developments from the past decade are presented for the first time outside technical research articles: discrete Helly numbers, new insights into sublinear functions, and best known bounds on the information and algorithmic complexity of mixed-integer convex optimization. Pedagogical explanations and more than 300 exercises make this book ideal for students and researchers.
Amitabh Basu is Professor of Applied Mathematics and Statistics at Johns Hopkins University. He has received the NSF CAREER award and the Egon Balas Prize from the INFORMS Optimization Society. He serves on the editorial boards of 'Mathematics of Operations Research,' 'Mathematical Programming,' 'SIAM Journal on Optimization,' and the 'MOS-SIAM Series on Optimization.'
1. Preliminaries; Part I. Structural Aspects: 2. Convex sets; 3. Convex functions; 4. Geometry of numbers; Part II. Optimization: 5. Ingredients of mathematical optimization; 6. Complexity of convex optimization with integer variables; 7. Certificates and duality; Hints to selected exercises; References; Index.
| Erscheinungsdatum | 31.01.2025 |
|---|---|
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 234 mm |
| Gewicht | 590 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| ISBN-10 | 1-108-83759-X / 110883759X |
| ISBN-13 | 978-1-108-83759-0 / 9781108837590 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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