Subdifferentials: Theory and Applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
323 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The subject of the present book is sub differential calculus. The main source of this branch of functional analysis is the theory of extremal problems. For a start, we explicate the origin and statement of the principal problems of sub differential calculus. To this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. Here X is a vector space and f : X --+ iR is a numeric function taking possibly infinite values. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i. e. , such an x that f(x) = inf f(X», if the latter exists. It is a rare occurrence to solve an arbitrary problem explicitly, i. e. to exhibit the value of the problem and one of its solutions. In this respect it becomes necessary to simplify the initial problem by reducing it to somewhat more manageable modifications formulated with the details of the structure of the objective function taken in due account. The conventional hypothesis presumed in attempts at theoretically approaching the reduction sought is as follows. Introducing an auxiliary function 1, one considers the next problem: x EX, f(x) -l(x) --+ inf. Furthermore, the new problem is assumed to be as complicated as the initial prob lem provided that 1 is a linear functional over X, i. e |
| Beschreibung: | 1 Online-Ressource (IX, 405 p) |
| ISBN: | 9789401102650 9789401041171 |
| DOI: | 10.1007/978-94-011-0265-0 |
Internformat
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| 500 | |a The subject of the present book is sub differential calculus. The main source of this branch of functional analysis is the theory of extremal problems. For a start, we explicate the origin and statement of the principal problems of sub differential calculus. To this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. Here X is a vector space and f : X --+ iR is a numeric function taking possibly infinite values. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i. e. , such an x that f(x) = inf f(X», if the latter exists. It is a rare occurrence to solve an arbitrary problem explicitly, i. e. to exhibit the value of the problem and one of its solutions. In this respect it becomes necessary to simplify the initial problem by reducing it to somewhat more manageable modifications formulated with the details of the structure of the objective function taken in due account. The conventional hypothesis presumed in attempts at theoretically approaching the reduction sought is as follows. Introducing an auxiliary function 1, one considers the next problem: x EX, f(x) -l(x) --+ inf. Furthermore, the new problem is assumed to be as complicated as the initial prob lem provided that 1 is a linear functional over X, i. e | ||
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Datensatz im Suchindex
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| doi_str_mv | 10.1007/978-94-011-0265-0 |
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| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401102650 9789401041171 |
| language | English |
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| spelling | Kusraev, A. G. Verfasser aut Subdifferentials: Theory and Applications by A. G. Kusraev, S. S. Kutateladze Dordrecht Springer Netherlands 1995 1 Online-Ressource (IX, 405 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 323 The subject of the present book is sub differential calculus. The main source of this branch of functional analysis is the theory of extremal problems. For a start, we explicate the origin and statement of the principal problems of sub differential calculus. To this end, consider an abstract minimization problem formulated as follows: x E X, f(x) --+ inf. Here X is a vector space and f : X --+ iR is a numeric function taking possibly infinite values. In these circumstances, we are usually interested in the quantity inf f( x), the value of the problem, and in a solution or an optimum plan of the problem (i. e. , such an x that f(x) = inf f(X», if the latter exists. It is a rare occurrence to solve an arbitrary problem explicitly, i. e. to exhibit the value of the problem and one of its solutions. In this respect it becomes necessary to simplify the initial problem by reducing it to somewhat more manageable modifications formulated with the details of the structure of the objective function taken in due account. The conventional hypothesis presumed in attempts at theoretically approaching the reduction sought is as follows. Introducing an auxiliary function 1, one considers the next problem: x EX, f(x) -l(x) --+ inf. Furthermore, the new problem is assumed to be as complicated as the initial prob lem provided that 1 is a linear functional over X, i. e Mathematics Functional analysis Operator theory Discrete groups Logic, Symbolic and mathematical Mathematical optimization Functional Analysis Optimization Convex and Discrete Geometry Operator Theory Mathematical Logic and Foundations Mathematik Subdifferential (DE-588)4404539-6 gnd rswk-swf Subdifferential (DE-588)4404539-6 s 1\p DE-604 Kutateladze, S. S. Sonstige oth https://doi.org/10.1007/978-94-011-0265-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kusraev, A. G. Subdifferentials: Theory and Applications Mathematics Functional analysis Operator theory Discrete groups Logic, Symbolic and mathematical Mathematical optimization Functional Analysis Optimization Convex and Discrete Geometry Operator Theory Mathematical Logic and Foundations Mathematik Subdifferential (DE-588)4404539-6 gnd |
| subject_GND | (DE-588)4404539-6 |
| title | Subdifferentials: Theory and Applications |
| title_auth | Subdifferentials: Theory and Applications |
| title_exact_search | Subdifferentials: Theory and Applications |
| title_full | Subdifferentials: Theory and Applications by A. G. Kusraev, S. S. Kutateladze |
| title_fullStr | Subdifferentials: Theory and Applications by A. G. Kusraev, S. S. Kutateladze |
| title_full_unstemmed | Subdifferentials: Theory and Applications by A. G. Kusraev, S. S. Kutateladze |
| title_short | Subdifferentials: Theory and Applications |
| title_sort | subdifferentials theory and applications |
| topic | Mathematics Functional analysis Operator theory Discrete groups Logic, Symbolic and mathematical Mathematical optimization Functional Analysis Optimization Convex and Discrete Geometry Operator Theory Mathematical Logic and Foundations Mathematik Subdifferential (DE-588)4404539-6 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Discrete groups Logic, Symbolic and mathematical Mathematical optimization Functional Analysis Optimization Convex and Discrete Geometry Operator Theory Mathematical Logic and Foundations Mathematik Subdifferential |
| url | https://doi.org/10.1007/978-94-011-0265-0 |
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