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CCA (Computational Convex Analysis) >> plq > plq_me_max_scale

# plq_me_max_scale

Piecewise linear quadratic (plq), Maximum scale for Moreau envelope

### Calling Sequence

    scale = plq_me_max_scale(plqf1, ..., plqfN)

### Parameters

plqf1 ... plqfN

  matrices. PLQ functions for which to compute the maximum scale.

scale

  constant. The maximum smoothing parameter that plq_me will accept over all the given functions.

### Description

This function computes the maximum smoothing parameter that may be passed as "lambda" or "mu" into plq_me such that a set of nonconvex functions have finite Moreau envelopes. Otherwise, if the smoothing parameter is too high, g* below will be infinite everywhere because a convex hull cannot be computed. The Moreau envelope formula is

### Examples

    f1 = [0,-1,0,0;%inf,-2,0,0];
    plq_me_max_scale(f1),          # -1/2/(-2) == 0.25
    f2 = [1,0,1,0;2,0,-1,2;%inf,-3,0,0];
    plq_me_max_scale(f2),          # -1/2/(-3) == 0.167
    plq_me_max_scale(f1, f2);      # 0.167

### See Also

- plq_function

### Authors

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

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