Duality Principles in Nonconvex Systems Theory, Methods and Applications
A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, varia...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer US
2000, 2000
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| Edition: | 1st ed. 2000 |
| Series: | Nonconvex Optimization and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Symmetry in Convex Systems
- 1. Mono-Duality in Static Systems
- 2. Bi-Duality in Dynamical Systems
- II Symmetry Breaking: Triality Theory in Nonconvex Systems
- 3. Tri-Duality in Nonconvex Systems
- 4. Multi-Duality and Classifications of General Systems
- III Duality in Canonical Systems
- 5. Duality in Geometrically Linear Systems
- 6. Duality in Finite Deformation Systems
- 7. Applications, Open Problems and Concluding Remarks
- Appendices
- A—Duality in Linear Analysis
- A.1 Linear spaces and duality
- A.2 Bilinear Forms and Inner Product Spaces
- A.3 Linear functionals and Dual spaces
- B—Linear Operators and Adjointness
- B.1 Linear Operators
- B.2 Adjoint Operators
- B.3 Duality Relations for Range and Nullspace
- C—Nonlinear Operators
- C.1 Operators on Finite-Dimensional Spaces
- C.2 Monotone and Pseudo-Monotone Operators on Banach Spaces
- C.3 Potential Operators and Duality Mappings
- References