Piecewise linear quadratic (plq), Lasry-Lions double envelope
plqg = plq_ll(plqf, lambda, mu)
matrix. A PLQ function.
constant. This value determines how close the Lasry-Lions envelope will be to the original function.
constant. This value determines the smoothness factor inside the nonconvex function (i.e. not on the convex hull). Note: mu > lambda.
matrix. The resulting PLQ function.
Computes the Lasry-Lions double envelope of a given PLQ function, using the formula (M is the Moreau envelope)
This algorithm, like its subroutines, runs in linear time.
plqf = [-1,0,-1,-1; 0,0,1,1; 1,0,-1,1; %inf,0,1,-1]; mu = 0.7; lambda = 0.4; plqg = plq_ll(plqf, lambda, mu); plq_plot(plqf, plqg, -3, 3); xtitle("Lasry-Lions double envelope"); | ![]() | ![]() |
Bryan Gardiner
, University of British Columbia, BC, Canada