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CCA (Computational Convex Analysis) >> opt > opt_ka

# opt_ka

Convex operators via optimization (OPT), Kernel average

### Calling Sequence

    [y, argmin] = opt_ka(f1, df1, domf1, f2, df2, domf2, g, dg, domg, x, lambda, output)

### Parameters

f1, f2, g

  Univariate functions, continuous but (potentially) nonsmooth.

df1, df2, dg

  Univariate functions: derivatives of f1, f2, g (respectively).

domf1, domf2, domg

  Domains of functions f1, f2, g (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 kernel average.

lambda

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

output

  0: no output, 1: progress bar.

y

  The values of the kernel average evaluated at x.

argmin

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

### Description

Computes the (kernel average) g-average of f1 and f2 evaluated on vector x, giving the values y such that

### Authors

- Yves Lucet, University of British Columbia, BC, Canada

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