Lectures on Convex Optimization

1. Front Matter

   Pages i-xxiii

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2. Black-Box Optimization

   1. Front Matter

      Pages 1-1

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   2. Nonlinear Optimization

      • Yurii Nesterov

      Pages 3-58

   3. Smooth Convex Optimization

      • Yurii Nesterov

      Pages 59-137

   4. Nonsmooth Convex Optimization

      • Yurii Nesterov

      Pages 139-240

   5. Second-Order Methods

      • Yurii Nesterov

      Pages 241-322

3. Structural Optimization

   1. Front Matter

      Pages 323-323

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   2. Polynomial-Time Interior-Point Methods

      • Yurii Nesterov

      Pages 325-421

   3. The Primal-Dual Model of an Objective Function

      • Yurii Nesterov

      Pages 423-487

   4. Optimization in Relative Scale

      • Yurii Nesterov

      Pages 489-570

4. Back Matter

   Pages 571-589

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This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.

Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

• complexity
• complexity theory
• graphs
• mathematical programming
• optimization
• Fast Gradient Methods
• Self-Concordant Functions
• Interior-Point Methods
• Smoothing Technique
• Cubic Regularization of Newton Method
• Optimization in Relative Scale
• MSC 2010 49M15, 49M29, 49N15, 65K05, 65K10, 90C25, 90C30, 90C46
• 90C51, 90C52, 90C60
• algorithm analysis and problem complexity

“It is a must-read for both students involved in the operations research programs, as well as the researchers in the area of nonlinear programming, in particular in convex optimization.” (Marcin Anholcer, zbMATH 1427.90003, 2020)

• CORE/INMA, Catholic University of Louvain, Louvain-la-Neuve, Belgium

  Yurii Nesterov

​Yurii Nesterov is a well-known specialist in optimization. He is an author of pioneering works related to fast gradient methods, polynomial-time interior-point methods, smoothing technique, regularized Newton methods, and others. He is a winner of several prestigious international prizes, including George Danzig prize (2000), von Neumann Theory prize (2009), SIAM Outstanding Paper Award (20014), and Euro Gold Medal (2016).

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