Necessary Conditions for an ExtremumCRC Press, 17 août 2020 - 248 pages This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems. |
Table des matières
INTRODUCTION ELEMENTS OF FUNCTIONAL ANALYSIS AND CONVEX SETS | 1 |
CHAPTER 1 PROPERTIES OF CONVEX FUNCTIONALS | 39 |
CHAPTER II CONVEX PROGRAMMING IN BANACH SPACES | 54 |
CHAPTER III QUASIDIFFERENTIABLE FUNCTIONALS | 68 |
CHAPTER IV NECESSARY CONDITIONS FOR AN EXTREMUM IN GENERAL MATHEMATICAL PROGRAMMING PROBLEMS | 82 |
CHAPTER V NECESSARY CONDITIONS FOR AN EXTREMUM IN CONCRETE PROBLEMS | 120 |
SHORT BIBLIOGRAPHY | 201 |
| 210 | |
NOTES AND SUPPLEMENTARY BIBLIOGRAPHY TO AMERICAN EDITION | 217 |
| 223 | |
| 226 | |
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Expressions et termes fréquents
according achieves Analysis applied approximation assume assumptions Banach space basic basis belongs bounded Chapter closed coincides compact compact set concept consider consists constraints construct contains continuous functions contradicts convergence convex cone convex functionals convex hull convex set corollary defined definition denote developed differential direction easy element entire equal equations equivalent exist numbers exists extremum fact formula functional u(x Further given holds implies independent inequality intersection introduced Lemma linear linear space linearly mathematical maximum principle means methods minimized moment problem Moreover n-dimensional necessary conditions norm obtain obvious operator optimal control positive preceding presented Proof properties proved relation represented respect satisfies sequence set of support side solution solving studied sufficiently small suppose Theorem Theorem 4.6 theory tion topology vectors virtue weak zero хо