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CCA (Computational Convex Analysis) >> plq > plq_ll

# plq_ll

Piecewise linear quadratic (plq), Lasry-Lions double envelope

### Calling Sequence

    plqg = plq_ll(plqf, lambda, mu)

### Parameters

plqf

  matrix. A PLQ function.

lambda

  constant. This value determines how close the Lasry-Lions envelope will be to the original function.

mu

  constant. This value determines the smoothness factor inside the nonconvex function (i.e. not on the convex hull). Note: mu > lambda.

plqg

  matrix. The resulting PLQ function.

### Description

Computes the Lasry-Lions double envelope of a given PLQ function, using the formula (M is the Moreau envelope)

This algorithm, like its subroutines, runs in linear time.

### Examples

    plqf = [-1,0,-1,-1; 0,0,1,1; 1,0,-1,1; %inf,0,1,-1];
    mu = 0.7;
    lambda = 0.4;
    plqg = plq_ll(plqf, lambda, mu);
    plq_plot(plqf, plqg, -3, 3);
    xtitle("Lasry-Lions double envelope");

### See Also

- plq_function

### Authors

`Bryan Gardiner`, University of British Columbia, BC, Canada

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