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Essential Mathematics for Convex Optimization

Authors

Fatma Kılınç-Karzan
, Carnegie Mellon University, Pennsylvania,
Arkadi Nemirovski
, Georgia Institute of Technology
Published 2025

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…

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Key features

  • Focuses on the mathematical foundations, providing a fresh look on convex analysis from the point of view of optimization
  • Covers modern topics such as conic programming, conic representations of convex sets and functions, and cone-constrained convex problems
  • Provides a rigorous yet accessible treatment based on linear algebra, calculus, and real analysis, lowering the background barrier for students
  • Over 170 exercises and over 30 'Facts' to prove, which trains readers to become active players in optimization, and not just mere consumers of its techniques
  • Includes appendices that cover all the prerequisites from linear algebra, real analysis, calculus, and symmetric matrices for the course

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