Optimality Conditions: Abnormal and Degenerate Problems

Capa
Springer Science & Business Media, 31/10/2000 - 299 páginas
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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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Índice

II
1
III
8
IV
11
V
15
VI
22
VII
23
VIII
31
IX
36
XXVI
147
XXVII
155
XXVIII
164
XXIX
167
XXX
174
XXXI
181
XXXII
183
XXXIII
188

X
41
XI
44
XII
53
XIII
60
XIV
69
XV
71
XVI
74
XVII
78
XVIII
89
XIX
92
XX
98
XXI
107
XXII
115
XXIII
123
XXIV
133
XXV
141
XXXIV
196
XXXV
198
XXXVI
208
XXXVII
221
XXXVIII
242
XXXIX
245
XL
249
XLI
258
XLII
265
XLIII
268
XLIV
279
XLV
287
XLVI
293
XLVII
297
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