convex optimization

#incomplete

convexity assumption

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

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

References:

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