This book is a comprehensive textbook on convex optimization, written by E. A. Voroncova, R. F. Hildbrand, A. V. Gasnikov, and F. S. Stonyakin. It is published by the Moscow Institute of Physics and Technology (National Research University) and is dedicated to students of the Physics and Technology School at MIPT who are studying the course "Optimization." The book covers the fundamentals of convex analysis and convex optimization, including topics such as convex sets, convex functions, cones, and order relations. It also discusses optimization problems with constraints, duality, and various numerical methods for solving convex optimization problems. The book provides a detailed treatment of convex optimization theory and its applications, including linear programming, quadratic programming, and conic programming. It also addresses robust optimization and provides a thorough explanation of the theory of accelerated gradient methods. The book is written in Russian and includes a detailed list of references and a comprehensive index. The authors emphasize the importance of convex optimization in practical applications and provide a solid foundation for further study in this field. The book is structured into chapters that cover the basics of convex analysis, convex optimization methods, and advanced topics in convex optimization. It is an essential resource for students and researchers in the field of optimization.This book is a comprehensive textbook on convex optimization, written by E. A. Voroncova, R. F. Hildbrand, A. V. Gasnikov, and F. S. Stonyakin. It is published by the Moscow Institute of Physics and Technology (National Research University) and is dedicated to students of the Physics and Technology School at MIPT who are studying the course "Optimization." The book covers the fundamentals of convex analysis and convex optimization, including topics such as convex sets, convex functions, cones, and order relations. It also discusses optimization problems with constraints, duality, and various numerical methods for solving convex optimization problems. The book provides a detailed treatment of convex optimization theory and its applications, including linear programming, quadratic programming, and conic programming. It also addresses robust optimization and provides a thorough explanation of the theory of accelerated gradient methods. The book is written in Russian and includes a detailed list of references and a comprehensive index. The authors emphasize the importance of convex optimization in practical applications and provide a solid foundation for further study in this field. The book is structured into chapters that cover the basics of convex analysis, convex optimization methods, and advanced topics in convex optimization. It is an essential resource for students and researchers in the field of optimization.