Optimization and Its Applications in Control and Data Sciences

1. Front Matter

   Pages i-xvii

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2. A New Adaptive Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization

   • Neculai Andrei

   Pages 1-16

3. On Methods of Terminal Control with Boundary-Value Problems: Lagrange Approach

   • Anatoly Antipin, Elena Khoroshilova

   Pages 17-49

4. Optimization of Portfolio Compositions for Small and Medium Price-Taking Traders

   • Alexander S. Belenky, Lyudmila G. Egorova

   Pages 51-117

5. Indirect Maximum Likelihood Estimation

   • Daniel Berend, Luba Sapir

   Pages 119-138

6. Lagrangian Duality in Complex Pose Graph Optimization

   • Giuseppe C. Calafiore, Luca Carlone, Frank Dellaert

   Pages 139-184

7. State-Feedback Control of Positive Switching Systems with Markovian Jumps

   • Patrizio Colaneri, Paolo Bolzern, José C. Geromel, Grace S. Deaecto

   Pages 185-219

8. Matrix-Free Convex Optimization Modeling

   • Steven Diamond, Stephen Boyd

   Pages 221-264

9. Invariance Conditions for Nonlinear Dynamical Systems

   • Zoltán Horváth, Yunfei Song, Tamás Terlaky

   Pages 265-280

10. Modeling of Stationary Periodic Time Series by ARMA Representations

    • Anders Lindquist, Giorgio Picci

    Pages 281-314

11. A New Two-Step Proximal Algorithm of Solving the Problem of Equilibrium Programming

    • Sergey I. Lyashko, Vladimir V. Semenov

    Pages 315-325

12. Nonparametric Ellipsoidal Approximation of Compact Sets of Random Points

    • Sergey I. Lyashko, Dmitry A. Klyushin, Vladimir V. Semenov, Maryna V. Prysiazhna, Maksym P. Shlykov

    Pages 327-340

13. Extremal Results for Algebraic Linear Interval Systems

    • Daniel N. Mohsenizadeh, Vilma A. Oliveira, Lee H. Keel, Shankar P. Bhattacharyya

    Pages 341-351

14. Applying the Gradient Projection Method to a Model of Proportional Membership for Fuzzy Cluster Analysis

    • Susana Nascimento

    Pages 353-380

15. Algorithmic Principle of Least Revenue for Finding Market Equilibria

    • Yurii Nesterov, Vladimir Shikhman

    Pages 381-435

16. The Legendre Transformation in Modern Optimization

    • Roman A. Polyak

    Pages 437-507

This book focuses on recent research in modern optimization and its implications in control and data analysis. This book is a collection of papers from the conference “Optimization and Its Applications in Control and Data Science” dedicated to Professor Boris T. Polyak, which was held in Moscow, Russia on May 13-15, 2015.

This book reflects developments in theory and applications rooted by Professor Polyak’s fundamental contributions to constrained and unconstrained optimization, differentiable and nonsmooth functions, control theory and approximation. Each paper focuses on techniques for solving complex optimization problems in different application areas and recent developments in optimization theory and methods. Open problems in optimization, game theory and control theory are included in this collection which will interest engineers and researchers working with efficient algorithms and software for solving optimization problems in market and data analysis. Theoreticians in operations research, applied mathematics, algorithm design, artificial intelligence, machine learning, and software engineering will find this book useful and graduate students will find the state-of-the-art research valuable.

• Data analysis
• Dynamical Systems
• Linear programming
• Markovian Jumps
• Nonconvex programming
• Nonlinear programming
• Nonparametric ellipsoidal approximation
• global optimization
• data structures

“This book, organized and nicely edited by Professor Goldengorin, reflects some recent advances in the areas of optimization, control, and data sciences in the directions largely initiated and developed by Boris Polyak over the years. … I would like to congratulate the editor and all the authors of the papers presented in the book on their excellent work to celebrate great achievements and scientific life of Boris Teodorovich Polyak.” (Boris S. Mordukhovich, Optimization Letters, Vol. 11, 2017)

• Department of Industrial and Systems Engineering, Ohio University, Athens, USA

  Boris Goldengorin

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