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CCA (Computational Convex Analysis) >> pl > pl_me_plt

# pl_me_plt

Parametric Moreau Envelope, PME algorithm

### Calling Sequence

    [M, z] = pl_me_plt(X, f, df)

### Parameters

X

  column vector. A grid of points on which the function is sampled.

f

  column vector. The value of the function on the grid X: usually Y(i)=f(X(i)) for some function f.

df

  column vector. The value of the derivative of the function f evaluated on X, which is also the slope.

### Description

Compute numerically the discrete Moreau envelope of a set of planar points (X(i),f(i)) at slopes S(j), i.e.

It reduces computation to computing the Legendre conjugate through the formula

Here the conjugate is derived by the Parametric Legendre Transform.

### Examples

    function y=f(x), y=0.5 * x.^2, endfunction;
    function s=df(x), s= x, endfunction;
    b=%T;n=8;
    X=(-n/2:1:n/2)';S=df(X);Y=f(X);
    [M,z] = pl_me_plt(X, f, df);

### See Also

- pl_me_direct
- pl_me_llt
- pl_me_nep
- pl_me_pe

### Authors

`Yves Lucet`, University of British Columbia, BC, Canada

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