proximal_operators

Factory functions for creating proximal operators.

Functions with convex_conj mean the proximal of the convex conjugate and are provided for convenience.

For more details see Proximal Operators and references therein. For more details on proximal operators including how to evaluate the proximal operator of a variety of functions see [PB2014].

References

[PB2014] Parikh, N, and Boyd, S. Proximal Algorithms. Foundations and Trends in Optimization, 1 (2014), pp 127-239.

Functions

combine_proximals(\*factory_list)	Combine proximal operators into a diagonal product space operator.
proj_l1(x[, radius, out])	Projection onto l1-ball.
proj_simplex(x[, diameter, out])	Projection onto simplex.
proximal_arg_scaling(prox_factory, scaling)	Calculate the proximal of function F(x * scaling).
proximal_box_constraint(space[, lower, upper])	Proximal operator factory for G(x) = ind(a <= x <= b).
proximal_composition(proximal, operator, mu)	Proximal operator factory of functional composed with unitary operator.
proximal_const_func(space)	Proximal operator factory of the constant functional.
proximal_convex_conj(prox_factory)	Calculate the proximal of the dual using Moreau decomposition.
proximal_convex_conj_kl(space[, lam, g])	Proximal operator factory of the convex conjugate of the KL divergence.
proximal_convex_conj_kl_cross_entropy(space)	Proximal factory of the convex conj of cross entropy KL divergence.
proximal_convex_conj_l1(space[, lam, g])	Proximal operator factory of the L1 norm/distance convex conjugate.
proximal_convex_conj_l1_l2(space[, lam, g])	Proximal operator factory of the L1-L2 norm/distance convex conjugate.
proximal_convex_conj_l2(space[, lam, g])	Proximal operator factory of the convex conj of the l2-norm/distance.
proximal_convex_conj_l2_squared(space[, lam, g])	Proximal operator factory of the convex conj of the squared l2-dist
proximal_convex_conj_linfty(space)	Proximal operator factory of the Linfty norm/distance convex conjugate.
proximal_huber(space, gamma)	Proximal factory of the Huber norm.
proximal_l1(space[, lam, g])	Proximal operator factory of the L1 norm/distance.
proximal_l1_l2(space[, lam, g])	Proximal operator factory of the group-L1-L2 norm/distance.
proximal_l2(space[, lam, g])	Proximal operator factory of the l2-norm/distance.
proximal_l2_squared(space[, lam, g])	Proximal operator factory of the squared l2-norm/distance.
proximal_linfty(space)	Proximal operator factory of the l_\infty-norm.
proximal_nonnegativity(space)	Function to create the proximal operator of G(x) = ind(x >= 0).
proximal_quadratic_perturbation(prox_factory, a)	Calculate the proximal of function F(x) + a * |x|^2 + <u,x>.
proximal_translation(prox_factory, y)	Calculate the proximal of the translated function F(x - y).