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Convexity and its Applications in Discrete and Continuous Optimization by Amitabh Basu (Johns Hopkins University) at Abbey's Bookshop,
Convexity and its Applications in Discrete and Continuous Optimization
— —
Amitabh Basu (Johns Hopkins University)

Convexity and its Applications in Discrete and Continuous Optimization

Amitabh Basu (Johns Hopkins University)

$105.95

Hardback

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English
Cambridge University Press
30 January 2025
Optimisation
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.
By:  
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Dimensions:   Height: 234mm,  Width: 157mm,  Spine: 24mm
Weight:   590g
ISBN:   9781108837590
ISBN 10:   110883759X
Pages:   328
Publication Date:  
Audience:   General/trade ,  ELT Advanced
Format:   Hardback
Publisher's Status:   Active
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.

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.'

Reviews for Convexity and its Applications in Discrete and Continuous Optimization

'Written by one of the most brilliant researchers in the field, this book provides an elegant, rigorous and original presentation of the theory of convexity, describing in a unified way its use in continuous and discrete optimization, and also covering some very recent advancements in these areas.' Marco Di Summa, University of Padua 'Convexity is central to most optimization algorithms. This book brings together classical and new developments at the interface between these two vibrant areas of mathematics. It is an essential reference for scholars in optimization. The numerous exercises make it an ideal textbook at the graduate and upper undergraduate levels.' Gérard Cornuéjols, Carnegie Mellon University


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