Essential Mathematics for Convex Optimization

‘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

Fatma Kılınç-Karzan is a Professor of Operations Research at Tepper School of Business, Carnegie Mellon University. She was awarded the 2015 INFORMS Optimization Society Prize for Young Researchers, the 2014 INFORMS JFIG Best Paper Award (with S. Yıldız), and an NSF CAREER Award in 2015. Her research focuses on foundational theory and algorithms for convex optimization and structured nonconvex optimization and their applications in optimization under uncertainty, machine learning, and business analytics. She has been an elected member on the councils of the Mathematical Optimization Society and INFORMS Computing Society, and has served on the editorial boards of MOS-SIAM Book Series on Optimization, MathProgA, MathOR, OPRE, SIAM J Opt, IJOC, and OMS.

Arkadi Nemirovski is the John P. Hunter, Jr. Chair and Professor of Industrial and Systems Engineering at Georgia Tech. He has co-authored six optimization textbooks including this one, and he has received many rewards for his contributions to the field, including the 1982 MPS-SIAM Fulkerson Prize (with L. Khachiyan and D. Yudin), the 1991 MPS-SIAM Dantzig Prize (with M. Grotschel), the 2003 INFORMS John von Neumann Theory Prize (with M. Todd), the 2019 SIAM Norbert Wiener Prize (with M. Berger), and the 2023 WLA Prize (with Yu. Nesterov). His research focuses on convex optimization (algorithmic design and complexity analysis, optimization under uncertainty, engineering applications) and nonparametric statistics. He is a member of the National Academy of Engineering, the American Academy of Arts and Sciences, and National Academy of Sciences.