#incomplete

convexity assumption

Given a function ff to minimize and a convex constraint set 𝒮\mathcal{S}, assume we have:

  • Function oracle: Evaluate f(𝐱)f(\mathbf{x}) for any 𝐱\mathbf{x}.
  • Gradient oracle: Evaluate ∇f(𝐱)∇f(\mathbf{x}) for any 𝐱\mathbf{x}.
  • projection oracle: Evaluate P𝒮(𝐱)P_\mathcal{S} (\mathbf{x}) for any 𝐱\mathbf{x}.
  • separation oracle

References:

  1. https://cims.nyu.edu/~cfgranda/pages/OBDA_fall17/notes/convex_optimization.pdf