Optimization: An Introduction

This book covers analytic methods to solve one-dimensional and multi-dimensional problems with or without possible constraints, iterative numerical techniques based on the gradient calculation or its estimation, and numerical methods that do not require the knowledge of gradient and use only comparative iterative tests. This book provides the reader with a basic introduction to some traditional parameter optimization techniques. The presented problems and their solution methods represent a core of the parameter optimization reign since the 17th century to the 1970s. Linear and integer programming via the simplex table is also introduced. Two simple selected problems that are solved using dynamic programming principles are also given to the reader. A general approach to constraints via penalty and barrier functions is introduced. A concise introduction to the decision and game theory concludes the book.

The book does not intend to provide the reader with a rigorous mathematic derivation of the presented methods. Its aim is instead to bring to the attention essential optimization tools for practitioners and undergraduate students and introduce selected well-established techniques to them when optimizing parameters of various models. Each method is described theoretically and supported by one or more numerical examples that vary from academic ones, through business economics to funny real-world problems that attract a broad audience. A sketch of Matlab code also follows numerical-based techniques. The author believes that the book finds its place in the libraries of many undergraduate students of various technical study programs and modern, thoughtful people worldwide, regardless of their expertise.

Libor Pekar received a B.S. degree in automation and informatics from Tomas Bata University (TBU) in Zlín in 2002, an M.S. degree in automation and control engineering in the consumption industry in 2005, and a Ph.D. degree in technical cybernetics from TBU in Zlín in 2013. He was appointed as an Associate Professor of machine and process control at TBU in Zlín in 2018. From 2006 to 2013, he worked as a Junior Lecturer at TBU in Zlín. He became a Senior Lecturer there in 2013. Since 2020, he has also worked as a Senior Lecturer at the College of Polytechnics Jihlava, Czech Republic. In 2024, he was appointed as a Guest Professor at the Beijing Institute of Technology, China, for five years.

Assoc. Prof. Pekar is the author of one book and eight book chapters and (co-)author of more than 50 journal articles and 80 conference papers. His research interests include analysis, modeling, identification, and control of time-delay systems, algebraic control methods, heat-exchanger processes, relay-based autotuning, and optimization techniques. He serves as an Academic Editor of Mathematical Problems in Engineering journal and Measurement and Control journal, a Topical Advisory Panel Member and a Lead Guest Editor of Mathematics journal, an Editorial Board Member of AppliedMath journal, and an Associate Editor of Frontiers in Energy Research journal and International Journal of Robotics and Control Systems. Assoc. Prof. Pekar is a member of IEEE, the American Chemical Society, and the Association for Computing Machinery. He has also served as a Reviewer for over 40 scientific journals, including Automatica, IEEE Transactions on Automatic Control, IEEE Transactions on Industrial Electronics, IEEE Control Systems Letters, Swarm and Evolutionary Computation, Applied Thermal Engineering, and ISA Transactions. Assoc. Prof. Pekar received the Laureate of the ASR Seminary Instrumentation and Control in 2007 and 2009, the Rectors’ Award for the best Ph.D. thesis at the Faculty of Applied Informatics TBU in Zlín in 2013, Best Reviewer Award from Control Theory and Technology journal in 2019, and the Outstanding Paper Award at the 1st World Conference on Multiphase Transportation, Conversion and Utilization of Energy in 2022.