Convex optimization theory
Enregistré dans:
| Hovedforfatter: | |
|---|---|
| Format: | Livre papier |
| Sprog: | Anglais |
| Udgivet: |
Belmont (Mass.) :
Athena Scientific
C 2009.
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| Serier: | Athena Scientific optimization and computation series
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| Fag: | |
| Autres localisations: | Voir dans le Sudoc |
Indholdsfortegnelse:
- 1. Basic concepts of convex analysis
- 1.1 Convex sets and functions
- 1.2 Convex and affine hulls
- 1.3 Relative interior and closure
- 1.4 Recession cones
- 1.5 Hyperplanes
- 1.6 Conjugate functions
- 1.7 Summary
- 2. Basic concepts of polyhedral convexity
- 2.1 extreme points
- 2.2 Polar cones
- 2.3 Polyhedral sets and functions
- 2.4 Polyhedral aspects of optimization
- 3. Basic concepts of convex optimization
- 3.1 Constrained optimization
- 3.2 Existence of optimal solutions
- 3.3 Partial minimization of convex functions
- 3.4 Saddle point and minimax theory
- 4. Geometric duality framework
- 4.1 Min common/max crossing duality
- 4.2 Some special cases
- 4.3 Strong duality theorem
- 4.4 Existence of dual optimal solutions
- 4.5 Duality and polyhedral convexity
- 4.6 Summary
- 5. duality and optimization
- 5.1 Nonlinear Farka's lemma
- 5.2 Linear programming duality
- 5.3 Convex programming duality
- 5.4 Subgradients and optimality conditions
- 5.5 Minimax theory
- 5.6 Theormes of the alternative
- 5.7 Nonconvex problems
- Appendix A. Mathematical background