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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

- plq_function
- plq_pa

### Authors

`Bryan Gardiner`, University of British Columbia, BC, Canada

### Bibliography

- W. L. Hare, 2009, The Proximal Average of Nonconvex Functions: A Proximal Stability Perspective, SIAM Journal on Optimization, 20(2), pp.650-666.

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