Roman Polyak is Emeritus professor of mathematics and operations research at George Mason University and visiting professor at Technion. He is the author/co-author of several monographs, books chapters, and journal papers. His expertise and interests are in linear and nonlinear programming, game theory, and mathematical economics. Dr. Polyak developed Nonlinear Rescaling (NR) theory and methods of constrained optimization.

“This book is meant as a textbook for a two-semester course on continuous optimization addressed to students studying mathematics. … The book may be interesting for readers wanting to learn more about some of the relatively recent achievements in nonlinear continuous optimization that have transformed the field.” (Andrzej Stachurski, Mathematical Reviews, April, 2022)“Throughout the book, the writing style is very clear, compact, self-contained, and easy to follow but at the same time mathematically rigorous. … This is a well-written book in the field of continuous optimization, and it is strongly recommended to students and researchers … . The organization and presentation … make it possible to use it both as a textbook for graduate students and as a reference book. Also, practitioners will find this book as a valuable reference.” (Samir Kumar Neogy, zbMATH 1473.90165, 2021)

• 1. Introduction.- 2. Elements of Calculus and Convex Analysis.- 3. Few Topics in Unconstrained Optimization.- 4. Optimization with Equality Constraints.- 5. Basics in Linear and Convex Optimization.-  Self-Concordant Functions and IPM Complexity.- 7. Nonlinear Rescaling. Theory and Methods.- 8. Realizations of the NR Principle.-  9. Lagrangian Transformation and Interior Ellipsoid Methods.- 10. Finding Nonlinear Equilibrium.- 11. (With Igor Griva) Applications and Numerical Results.- Concluding Remarks.- Appendix.- References.

Roman Polyak is Emeritus professor of mathematics and operations research at George Mason University and visiting professor at Technion. He is the author/co-author of several monographs, books chapters, and journal papers. His expertise and interests are in linear and nonlinear programming, game theory, and mathematical economics. Dr. Polyak developed Nonlinear Rescaling (NR) theory and methods of constrained optimization.

“This book is meant as a textbook for a two-semester course on continuous optimization addressed to students studying mathematics. … The book may be interesting for readers wanting to learn more about some of the relatively recent achievements in nonlinear continuous optimization that have transformed the field.” (Andrzej Stachurski, Mathematical Reviews, April, 2022)“Throughout the book, the writing style is very clear, compact, self-contained, and easy to follow but at the same time mathematically rigorous. … This is a well-written book in the field of continuous optimization, and it is strongly recommended to students and researchers … . The organization and presentation … make it possible to use it both as a textbook for graduate students and as a reference book. Also, practitioners will find this book as a valuable reference.” (Samir Kumar Neogy, zbMATH 1473.90165, 2021)

• 1. Introduction.- 2. Elements of Calculus and Convex Analysis.- 3. Few Topics in Unconstrained Optimization.- 4. Optimization with Equality Constraints.- 5. Basics in Linear and Convex Optimization.-  Self-Concordant Functions and IPM Complexity.- 7. Nonlinear Rescaling. Theory and Methods.- 8. Realizations of the NR Principle.-  9. Lagrangian Transformation and Interior Ellipsoid Methods.- 10. Finding Nonlinear Equilibrium.- 11. (With Igor Griva) Applications and Numerical Results.- Concluding Remarks.- Appendix.- References.