function ProxFS = prox_conjugate(ProxF)
% prox_conjugate - compute the proximal operator of the Legendre-Fenchel conjugate F^* through Moreau identity.
%
%   ProxFS = prox_conjugate(ProxF);
%
%   Compute the proximity callback of the Legendre-Fenchel conjugate given the proximity
%   callback of the primal function.
%
%   Use Moreau identity:
%       x = Prox_{tau*F^*}(x) + tau*Prox_{F/tau}(x/tau)
%

ProxFS = @(y,sigma)y-sigma*ProxF(y/sigma,1/sigma);