The Hausdorff error for ℓ_p-norm based outer approximations in convex vector optimization converges at the optimal rate O(k^{2/(1-q)}) independently of p.
Adaptive metrics for norm-minimization-based outer approximation in convex vector optimization,
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Convergence Rates for $\ell_p$ Norm Minimization in Convex Vector Optimization
The Hausdorff error for ℓ_p-norm based outer approximations in convex vector optimization converges at the optimal rate O(k^{2/(1-q)}) independently of p.