Convexity and its Applications in Discrete and Continuous Optimization (Hardcover)

Amitabh Basu

ISBN 10: 110883759X / ISBN 13: 9781108837590

Editore: Cambridge University Press, Cambridge, 2025

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Hardcover. 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. 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. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Codice articolo 9781108837590

Dati bibliografici

• Titolo: Convexity and its Applications in Discrete and Continuous Optimization (Hardcover)
• Editore: Cambridge University Press, Cambridge
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 110883759X
• ISBN 13: 9781108837590
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

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.