Scilab Function
Last update : 11/08/2008

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

Calling Sequence

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

Parameters

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.

    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.

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,  

Author

Bryan Gardiner, University of British Columbia, BC, Canada