plq_me_max_scale — Piecewise linear quadratic (plq), Maximum scale for Moreau envelope
scale = plq_me_max_scale(plqf1, ..., plqfN)
matrices. PLQ functions for which to compute the maximum scale.
constant. The maximum smoothing parameter that plq_me will accept over all the given functions.
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.
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