<< plq_function plq plq_gph >>

CCA (Computational Convex Analysis) >> plq > plq_gpa

plq_gpa

Piecewise linear quadratic (plq), generalized proximal average

Calling Sequence

pa = plq_gpa(p0, p1, lambda, r)

Parameters

p0, p1

matrices. PLQ functions.

lambda

constant in [0,1]. lambda1 = 1 - lambda. lambda2 = lambda.

r

positive constant. Parameter to the Moreau envelope.

pa

matrix. The non-convex proximal average of two PLQ functions computed via formula given below

Description

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.

Examples

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"]);

See Also

Authors

Bryan Gardiner, University of British Columbia, BC, Canada

Bibliography


Report an issue
<< plq_function plq plq_gph >>