Convex optimization algorithms

Convex optimization algorithms

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Auteur principal : Bertsekas Dimitri P. (Auteur)
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 :
Optimisation mathématique
Fonctions convexes
Programmation non linéaire
Algorithme > Convexe > Optimisation
  • 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