Convex optimization theory

Convex optimization theory

Enregistré dans:
Détails bibliographiques
Auteur principal : Bertsekas Dimitri P. (Auteur)
Format : Livre
Langue : anglais
Titre complet : Convex optimization theory / Dimitri P. Bertsekas
Publié : Belmont (Mass.) : Athena Scientific , copyright 2009
Description matérielle : 1 vol. (X-246 p.)
Collection : Athena scientific optimization and computation series
Sujets :
Optimisation mathématique
Dualité, Principe de (mathématiques)
  • 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