P^N — the polytope of optimal subgradient methods

minimax-optimal subgradient methods

Every minimax-optimal fixed-step method for Lipschitz convex minimization corresponds to a unique set of dual multipliers in this polytope.

edges:

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each vertex corresponds to a mapping below

step-size matrix of the selected vertex (D = M = 1)

Drori–Taylor · the map s(j)=j+1

Averaged Subgradient · the map s(j)=N

Zamani–Glineur · barycenter, not a vertex