pl_me_plt — Parametric Moreau Envelope, PME algorithm
[M, z] = pl_me_plt(X, f, df)
column vector. A grid of points on which the function is sampled.
column vector. The value of the function on the grid X: usually Y(i)=f(X(i)) for some function f.
column vector. The value of the derivative of the function f evaluated on X, which is also the slope.
Compute numerically the discrete Moreau envelope of a set of planar points (X(i),f(i)) at slopes S(j), i.e.
2 M(j) = min f(i) + || s(j) - x(i) ||. i
It reduces computation to computing the Legendre conjugate through the formula
2 2 M(j) = s(j) - 2 g*(j) with g*(j) = max [ s(j) * x(i) - 1/2 * (x(i) + f(i)) ], i where the conjugate is derived by the Parametric Legendre Transform.
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