= Second-order cone reformulation of one-sided quadratic denoising
The objective $\|u-g\|_2+\lambda\sum_i((Gu)_i)_+^2$ has the exact lift $\min t+\lambda\sum_iq_i$ with $(t,u-g)\in\mathcal Q_{n+1}$, $((q_i+1)/2,(q_i-1)/2,a_i)\in\mathcal Q_3$, $a_i\geq0$ and $a_i\geq(Gu)_i$. Every lifted feasible value bounds the original objective, and choosing tight epigraph variables proves equality. The product-cone barrier parameter is $4n+2$: two for each Lorentz block and one for each orthant slack. The fidelity norm remains unsquared, and negative derivatives remain unpenalized.
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