OAI/Geometry/Convex/GeneralMahler/Proj.lean

GitHub source file

18 declarations, 0 contain sorry, 0 declared as axioms

Euclidean projection onto a closed convex cone and Moreau decomposition.

  1. def OAI.GeneralMahler.coneProj line 11
  2. theorem OAI.GeneralMahler.proj_mem line 17
  3. theorem OAI.GeneralMahler.proj_vi line 20
  4. theorem OAI.GeneralMahler.proj_unique line 26
  5. theorem OAI.GeneralMahler.proj_of_mem line 38
  6. theorem OAI.GeneralMahler.proj_orthogonal line 41
  7. theorem OAI.GeneralMahler.proj_residual_dual line 48
  8. theorem OAI.GeneralMahler.proj_moreau line 56
  9. lemma OAI.GeneralMahler.proj_zero_of_dual line 66
  10. theorem OAI.GeneralMahler.proj_firm line 72
  11. theorem OAI.GeneralMahler.coneProj_lip line 81
  12. def OAI.GeneralMahler.energy line 88
  13. lemma OAI.GeneralMahler.energy_lower line 90
  14. theorem OAI.GeneralMahler.energy_eq line 97
  15. theorem OAI.GeneralMahler.energy_minorant line 103
  16. theorem OAI.GeneralMahler.energy_hasFDeriv line 109
  17. theorem OAI.GeneralMahler.coneProj_fderiv_symmetric line 128
  18. theorem OAI.GeneralMahler.coneProj_fderiv_pos line 139