Convex optimization algorithms
Enregistré dans:
Auteur principal : | |
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Format : | Livre |
Langue : | anglais |
Titre complet : | Convex optimization algorithms / Dimitri P. Bertsekas |
Publié : |
Nashua, NH :
Athena Scientific
, [2015] |
Description matérielle : | 1 vol. (XII-564 p.) |
Sujets : |
- 1. Convex optimization models : an overview
- 1.1 Lagrange duality
- 1.2 Fenchel duality and conic programming
- 1.3 Additive cost problems
- 1.4 Large number of constraints
- 1.5 Exact penalty functions
- 1.6 Notes, sources, and exercises
- 2. Optimization algorithms : an overview
- 2.1 Iterative descent algorithms
- 2.2 Approximation methods
- 2.3 Notes, sources, and exercises
- 3. Subgradient methods
- 3.1 Subgradients of convex real-valued functions
- 3.2 Convergence analysis of subgradient methods
- 3.3 E-subgradient methods
- 3.4 Notes, sources, and exercises
- 4. Polyhedral approximation methods
- 4.1 Outer linearization - cutting plane methods
- 4.2 Inner linearization - simplicial decomposition
- 4.3 Duality of outer and inner linearization
- 4.4 Generalized polyhedral approximation
- 4.5 Generalized simplicial decomposition
- 4.6 Polyhedral approximation for conic programming
- 4.7 Notes, sources, and exercises
- 5. Proximal algorithms
- 5.1 Basic theory of proximal algorithms
- 5.2 Dual proximal algorithms
- 5.3 Proximal algorithms with linearization
- 5.4 Alternating direction methods of multipliers
- 5.5 Notes, sources, and exercises
- 6. Additional algorithmic topics
- 6.1 Gradient projection methods
- 6.2 Gradient projection with extrapolation
- 6.3 Proximal gradient methods
- 6.4 Incremental subgradient proximal methods
- 6.5 Coordinate descent methods
- 6.6 Generalized proximal methods
- 6.7 E-descent and extended monotropic programming
- 6.8 Interior point methods
- 6.9 Notes, sources, and exercises
- Appendix A. Mathematical background
- Appendix B. Convex optimization theory : a summary