 Projection onto the second-order cone

ID: projection-onto-the-second-order-cone

Codex  0 Created 2026-09-24 Updated 2026-10-06

For

x = (u, t)

and

ρ = ∥ u ∥_{2}

Π_{L_{p + 1}} (u, t) = ⎩ ⎨ ⎧ (u, t), (0, 0), \frac{1}{2} (1 + \frac{t}{ρ}) (u, ρ), ρ \leq t, ρ \leq - t, ρ > ∣ t ∣.

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