Unlocbox - Proximal operators

The proximal operator of function f evaluated in z is the solution of the folowing equation:

\begin{equation*} prox_{f, \gamma }(z)=\min_z \frac{1}{2} \|x-z\|_2^2 + \gamma f(z) \end{equation*}

Here are a list of common usual proximal operators available in the UnLocBoX. We remember the reader that projections are particular cases of proximal operators.

General Proximal operators

prox_l0 - Proximal operator of the L0 norm
prox_l1 - Proximal operator of the L1 norm
prox_l2 - Proximal operator of the L2 norm
prox_l2grad - Proximal operator of the L2 norm of the gradient
prox_l2gradfourier - Proximal operator of the L2 norm of the gradient in the Fourier domain
prox_linf1 - Proximal operator of the Linf1 norm
prox_l21 - Proximal operator of the L21 norm
prox_l12 - Proximal operator of the LP norm
prox_nuclearnorm - Proximal operator of the nuclear norm
prox_nuclearnorm_block - Proximal operator of the nuclear norm by block
prox_tv - Proximal operator of the TV norm
prox_tv3d - Proximal operator of the 3D TV norm
prox_tv1d - Proximal operator of the 1D TV norm
prox_tv4d - Proximal operator of the 4D TV norm
prox_sum_log - Proximal operor for the sum of logarithms.
prox_sum_log_norm2 - Proximal operator of log-barrier - sum(log(x))

Projection operators

proj_b1 - Projection on a B1-Ball
proj_b2 - Projection on a B2-Ball
proj_box - Bound the value of x
proj_nuclearnorm - Projection operator of the nuclear norm
proj_spsd - Projection onto the semi definite symetric positive set
proj_linear_eq - Projection onto a linear set of equalities
proj_linear_ineq - Projection onto a linear set of inequalities

Proximal tools

prox_sumg - Proximal operator of a sum of function
prox_adjoint - Proximal operator of the adjoint of a function
prox_add_2norm - Proximal operator
prox_fax - Proximal operator of f(Ax)

For help, bug reports, suggestions etc. please send email to unlocbox (at) groupes (dot) epfl (dot) ch