This textbook, "Convex Optimization," is authored by E. A. Vorontsova, R. F. Hillerbrand, A. V. Gaskin, and F. S. Stonyakina, and published by Moscow Institute of Physics and Technology (National Research University) in 2021. It covers the fundamentals of convex optimization, including convex analysis and numerical methods, and is designed for third-year students of the Physics and Technology Faculty at the Moscow Institute of Physics and Technology (MIPT). The book emphasizes the importance of convex optimization due to its rich theoretical foundation and practical effectiveness. It discusses various aspects of convex optimization, such as convex sets, functions, cones, and order relations, as well as techniques for constructing convex functions. The authors also delve into advanced topics like conic programming, robust optimization, and accelerated gradient methods. Key features of the book include: - A comprehensive treatment of convex optimization, including both theoretical foundations and practical applications. - Detailed explanations of numerical methods for solving convex optimization problems. - Advanced material on conic optimization and robust optimization, which are not commonly covered in introductory texts. - Examples and applications to illustrate the practical use of convex optimization in various fields. The textbook is intended to serve as a fundamental resource for students studying optimization, providing a solid foundation for further research and application in this field.This textbook, "Convex Optimization," is authored by E. A. Vorontsova, R. F. Hillerbrand, A. V. Gaskin, and F. S. Stonyakina, and published by Moscow Institute of Physics and Technology (National Research University) in 2021. It covers the fundamentals of convex optimization, including convex analysis and numerical methods, and is designed for third-year students of the Physics and Technology Faculty at the Moscow Institute of Physics and Technology (MIPT). The book emphasizes the importance of convex optimization due to its rich theoretical foundation and practical effectiveness. It discusses various aspects of convex optimization, such as convex sets, functions, cones, and order relations, as well as techniques for constructing convex functions. The authors also delve into advanced topics like conic programming, robust optimization, and accelerated gradient methods. Key features of the book include: - A comprehensive treatment of convex optimization, including both theoretical foundations and practical applications. - Detailed explanations of numerical methods for solving convex optimization problems. - Advanced material on conic optimization and robust optimization, which are not commonly covered in introductory texts. - Examples and applications to illustrate the practical use of convex optimization in various fields. The textbook is intended to serve as a fundamental resource for students studying optimization, providing a solid foundation for further research and application in this field.