Piecewise linear quadratic (plq), generalized proximal average
pa = plq_gpa(p0, p1, lambda, r)
matrices. PLQ functions.
constant in [0,1]. lambda1 = 1 - lambda. lambda2 = lambda.
positive constant. Parameter to the Moreau envelope.
Computes the nonconvex proximal average of two (potentially nonconvex) PLQ functions p0 and p1, via the formula
where M[k] is the Moreau envelope with smoothing parameter k.
This algorithm runs in O(n + m) time, where n and m are the number of pieces in p0 and p1, respectively.
p0 = [0,0,0.5,-1; %inf,0,-0.5,-1]; p1 = [%inf,0.25,0,0]; pa = plq_gpa(p0,p1,0.5,1), scf(); plq_plotMultiple(-5, 5, p0, p1, pa); legend(["p0", "p1", "pa"]); | ![]() | ![]() |
Bryan Gardiner
, University of British Columbia, BC, Canada