Optimization: 100 Examples is a book devoted to the analysis of scenarios for which the use of well-known optimization methods encounter certain difficulties. Analysing such examples allows a deeper understanding of the features of these optimization methods, including the limits of their applicability. In this way, the book seeks to stimulate further development and understanding of the theory of optimal control. The study of the presented examples makes it possible to more effectively diagnose problems that arise in the practical solution of optimal control problems, and to find ways to overcome the difficulties that have arisen.
Features
- Vast collection of examples
- Simple. accessible presentation
- Suitable as a research reference for anyone with an interest in optimization and optimal control theory, including mathematicians and engineers
- Examples differ in properties, i.e. each effect for each class of problems is illustrated by a unique example.
Part I. Minimization of Functions of One Variable. 1. Fermat theorem. 2. Additions. Part II. Optimal Control Problems for Systems with a Free Finite State. 3. Maximum principle. 4. Alternative methods. 5. Uniqueness and Sufficiency. 6. Singular Controls. 7. Unsolvability of Optimal Control Problems. 8. Ill-posed Optimal Control Problems. Part III. Optimal Control Problems for Systems with a Fixed Final State. 9. Maximum Principle for Systems with a Fixed Final State. 10. Addition. 11. Counterexamples of Optimal Control Problems with a Fixed Final State. Part IV. Optimal Control Problems for Systems with Isoperimetric Conditions. 13. Optimization of Systems with Isoperimetric Conditions. 14. Absence of Sufficiency and Uniqueness in Problems with Isoperimetric Conditions. 15. Different Counterexamples for Optimization Problems with Isoperimetric Conditions. Part V. Optimal Control Problems with a Free Initial State. 16. Optimal control systems with a free initial state. 17. Different Optimal Control Problems for Systems with a Free Initial State.
Biography
Simon Serovajsky is a professor of mathematics at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimization and optimal control theory, mathematical physics, mathematical modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.
