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CCA (Computational Convex Analysis) >> opt > opt_pa

opt_pa

Convex operators via optimization (OPT), Proximal average

Calling Sequence

[y, argmin] = opt_pa(f1, df1, domf1, f2, df2, domf2, x, lambda, output)

Parameters

f1, f2

Univariate functions, continuous but (potentially) nonsmooth.

df1, df2

Univariate functions: derivatives of f1 and f2 (respectively).

domf1, domf2

Domains of functions f1, f2 (set of points where function is finite). Domains are stored as intervals I=[lb,ub] with ub<lb storing an empty set.

x

Vector of points at which to evaluate the proximal average.

lambda

real number. lambda1 = 1 - lambda. lambda2 = lambda.

output

0: no output, 1: progress bar.

y

The values of the proximal average evaluated at x.

argmin

A point at which the proximal average attains its minimum, for each x.

Description

Computes the (lambda1,lambda2) proximal average of f1 and f2 evaluated on vector x, giving the values y such that

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