Convex operators via optimization (OPT), Proximal average
[y, argmin] = opt_pa(f1, df1, domf1, f2, df2, domf2, x, lambda, output)
Univariate functions, continuous but (potentially) nonsmooth.
Univariate functions: derivatives of f1 and f2 (respectively).
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.
Vector of points at which to evaluate the proximal average.
real number. lambda1 = 1 - lambda. lambda2 = lambda.
0: no output, 1: progress bar.
The values of the proximal average evaluated at x.
A point at which the proximal average attains its minimum, for each x.
Computes the (lambda1,lambda2) proximal average of f1 and f2 evaluated on vector x, giving the values y such that