Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2002
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
60 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Many questions dealing with solvability, stability and solution methods for variational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a reformulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differentiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical instrument dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not continuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including "Newton maps" and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its implication to implicit functions |
| Beschreibung: | 1 Online-Ressource (XXVIII, 333 p) |
| ISBN: | 9780306476167 9781402005503 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/b130810 |
Internformat
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Datensatz im Suchindex
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| isbn | 9780306476167 9781402005503 |
| issn | 1571-568X |
| language | English |
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| series2 | Nonconvex Optimization and Its Applications |
| spelling | Klatte, Diethard 1950- Verfasser (DE-588)1020724285 aut Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications by Diethard Klatte, Bernd Kummer Boston, MA Springer US 2002 1 Online-Ressource (XXVIII, 333 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 60 1571-568X Many questions dealing with solvability, stability and solution methods for variational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a reformulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differentiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical instrument dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not continuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including "Newton maps" and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its implication to implicit functions Mathematics Functional analysis Computer science / Mathematics Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Informatik Mathematik Nichtglatte Optimierung (DE-588)4120798-1 gnd rswk-swf Nichtglatte Optimierung (DE-588)4120798-1 s 1\p DE-604 Kummer, Bernd Sonstige oth Nonconvex Optimization and Its Applications 60 (DE-604)BV010085908 60 https://doi.org/10.1007/b130810 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klatte, Diethard 1950- Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications Nonconvex Optimization and Its Applications Mathematics Functional analysis Computer science / Mathematics Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Informatik Mathematik Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| subject_GND | (DE-588)4120798-1 |
| title | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications |
| title_auth | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications |
| title_exact_search | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications |
| title_full | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications by Diethard Klatte, Bernd Kummer |
| title_fullStr | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications by Diethard Klatte, Bernd Kummer |
| title_full_unstemmed | Nonsmooth Equations in Optimization Regularity, Calculus, Methods and Applications by Diethard Klatte, Bernd Kummer |
| title_short | Nonsmooth Equations in Optimization |
| title_sort | nonsmooth equations in optimization regularity calculus methods and applications |
| title_sub | Regularity, Calculus, Methods and Applications |
| topic | Mathematics Functional analysis Computer science / Mathematics Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Informatik Mathematik Nichtglatte Optimierung (DE-588)4120798-1 gnd |
| topic_facet | Mathematics Functional analysis Computer science / Mathematics Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Computational Mathematics and Numerical Analysis Approximations and Expansions Functional Analysis Informatik Mathematik Nichtglatte Optimierung |
| url | https://doi.org/10.1007/b130810 |
| volume_link | (DE-604)BV010085908 |
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