## Name

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

<listitem>

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.

        Moreau envelope formula:
        M[lambda](s) = (1/2lambda)||s||^2 - (1/lambda)g*[lambda](s),
        where g[lambda](x) = (1/2)*||x||^2 + lambda*f(x),
          and * represents the Fenchel Conjugate.

</listitem>

## 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