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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.

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


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