Optimality conditions : abnormal and degenerate problems

Author(s)

• Aruti︠u︡nov, A. V. (Aram Vladimirovich)

Bibliographic Information

Optimality conditions : abnormal and degenerate problems

Aram V. Arutyunov ; [translated by S.A. Vakhrameev]

（Mathematics and its applications, v. 526）

Kluwer Academic Publishers, 2000

• : alk. paper

Other Title

Uslovii︠a︡ ėkstremuma

Uniform Title

Uslovii︠a︡ ėkstremuma

Note

Includes bibliographical references and index

Description and Table of Contents

Description

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.

Table of Contents

Preface. 1. Extremal Problems with Constraints. 2. Optimal Control Problem. Pontryagin Maximum Principle. 3. Degenerate Quadratic Forms of the Calculus of Variations. 4. Study of Mappings in a Neighborhood of an Abnormal Point. References. Index. List of Notation.

by "Nielsen BookData"

Details

• NCID: BA49478412
• ISBN:
  • 0792366557
• LCCN: 00046975
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Dordrecht
• Pages/Volumes: x, 299 p.
• Size: 25 cm
• Classification:
  • LCC : QA402.5
  • DC21 : 519.3
• Subject Headings:
  • LCSH : Mathematical optimization
  • LCSH : Maxima and minima
  • LCSH : Calculus of variations
  • LCSH : Extremal problems (Mathematics)
• Parent Bibliography ID:
  • BA00044495