Ebook: Optimality Conditions: Abnormal and Degenerate Problems

This book is devoted to one of the main questions of the theory of extremal prob­ lems, namely, to necessary and sufficient extremality conditions. It is intended mostly for mathematicians and also for all those who are interested in optimiza­ tion problems. The book may be useful for advanced students, post-graduated students, and researchers. The book consists of four chapters. In Chap. 1 we study the abstract minimization problem with constraints, which is often called the mathemati­ cal programming problem. Chapter 2 is devoted to one of the most important classes of extremal problems, the optimal control problem. In the third chapter we study one of the main objects of the calculus of variations, the integral quadratic form. In the concluding, fourth, chapter we study local properties of smooth nonlinear mappings in a neighborhood of an abnormal point. The problems which are studied in this book (of course, in addition to their extremal nature) are united by our main interest being in the study of the so called abnormal or degenerate problems. This is the main distinction of the present book from a large number of books devoted to theory of extremal problems, among which there are many excellent textbooks, and books such as, e.g., [13, 38, 59, 78, 82, 86, 101, 112, 119], to mention a few.

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This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.
Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.

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This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.
Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Content:
Front Matter....Pages i-x
Extremal Problems with Constraints....Pages 1-87
Optimal Control Problem. Pontryagin maximum Principle....Pages 89-179
Degenerate Quadratic Forms of the Calculus of Variations....Pages 181-244
Study of Mappings in a Neighborhood of an Abnormal Point....Pages 245-285
Back Matter....Pages 287-299

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This book is devoted to one of the main questions of the theory of extremal problems, namely, to necessary and sufficient extremality conditions. The book consists of four parts. First, the abstract minimization problem with constraints is studied. The next chapter is devoted to one of the most important classes of extremal problems, the optimal control problem. Next, one of the main objects of the calculus of variations is studied, the integral quadratic form. Finally, local properties of smooth nonlinear mappings in a neighborhood of an abnormal point will be discussed.
Audience: The book is intended for researchers interested in optimization problems. The book may also be useful for advanced students and postgraduate students.
Content:
Front Matter....Pages i-x
Extremal Problems with Constraints....Pages 1-87
Optimal Control Problem. Pontryagin maximum Principle....Pages 89-179
Degenerate Quadratic Forms of the Calculus of Variations....Pages 181-244
Study of Mappings in a Neighborhood of an Abnormal Point....Pages 245-285
Back Matter....Pages 287-299
....