- Textbook
- Publisher:
- Cambridge University Press
- Online publication date:
- October 2025
- Print publication year:
- 2025
- Online ISBN:
- 9781009510561
Essential Mathematics for Convex Optimization
Book description
With an emphasis on timeless essential mathematical background for optimization, this textbook provides a comprehensive and accessible introduction to convex optimization for students in applied mathematics, computer science, and engineering. Authored by two influential researchers, the book covers both convex analysis basics and modern topics such as conic programming, conic representations of convex sets, and cone-constrained convex problems, providing readers with a solid, up-to-date understanding of the field. By excluding modeling and algorithms, the authors are able to discuss the theoretical aspects in greater depth. Over 170 in-depth exercises provide hands-on experience with the theory, while more than 30 'Facts' and their accompanying proofs enhance approachability. Instructors will appreciate the appendices that cover all necessary background and the instructors-only solutions manual provided online. By the end of the book, readers will be well equipped to engage with state-of-the-art developments in optimization and its applications in decision-making and engineering.
Reviews
‘This new book by Fatma Kılınç-Karzan and Arkadi Nemirovski is an important contribution to the field of optimization, offering valuable insights for both theoretical research and practical applications. This thorough volume starts with the basics of convex analysis and extends to recent developments in cone-constrained convex problems. The authors include many interesting exercises that help expand on the topics discussed. Additionally, the appendices contain useful supplementary materials that enhance the overall value of the book’
Yurii Nesterov - Professor at Corvinus University of Budapest, Emeritus Professor at Catholic University of Louvain, Belgium
‘This is a well-structured textbook on the mathematical foundations of convex optimization. It focuses on the structure of convex sets and functions, separation theorems, subgradients, and the theory of duality. The treatment is rigorous but readable, balancing clarity with depth.’
Osman Güler - University of Maryland, Baltimore County
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