PyProximal API

The Application Programming Interface (API) of PyProximal is composed of 3 elements:

• Orthogonal projections

• Proximal operators

• Solvers

Orthogonal projections

AffineSetProj(Op, b, niter)	Affine set projection.
BoxProj([lower, upper])	Box orthogonal projection.
EuclideanBallProj(center, radius)	Euclidean ball projection.
HankelProj()	Hankel matrix projection.
HyperPlaneBoxProj(coeffs, scalar[, lower, ...])	Orthogonal projection of the intersection between a Hyperplane and a Box.
IntersectionProj(k, n, sigma[, niter, tol])	Intersection of multiple convex sets
L0BallProj(radius)	\(L_0\) ball projection.
L01BallProj(radius)	\(L_{0,1}\) ball projection.
L1BallProj(n, radius[, maxiter, xtol])	\(L_1\) ball projection.
NuclearBallProj(n, radius[, maxiter, xtol])	Nuclear ball projection
SimplexProj(n, radius[, maxiter, xtol])	Simplex projection.

Proximal operators

Templates

ProxOperator([Op, hasgrad])

Common interface for proximal operators of a function.

moreau(prox, x, tau[, tol, raiseerror, verb])

Moreau Identity.

Vector

Convex

AffineSet(Op, b, niter)	Affine set proximal operator.
Box([lower, upper])	Box proximal operator.
Euclidean([sigma])	Euclidean norm proximal operator.
EuclideanBall(center, radius)	Euclidean ball proximal operator.
Hankel(dim)	Hankel proximal operator.
Huber(alpha)	Huber norm proximal operator.
Intersection(k, n, sigma[, niter, tol, call])	Intersection of multiple convex sets operator.
L0([sigma])	\(L_0\) norm proximal operator.
L0Ball(radius)	\(L_0\) ball proximal operator.
L01Ball(ndim, radius)	\(L_{0,1}\) ball proximal operator.
L1([sigma, g])	L1 norm proximal operator.
L1Ball(n, radius[, maxiter, xtol])	L1 ball proximal operator.
L2([Op, b, q, sigma, alpha, qgrad, niter, ...])	L2 Norm proximal operator.
L2Convolve(h[, b, nfft, sigma, dims, dir])	L2 Norm proximal operator with convolution operator
L21(ndim[, sigma])	\(L_{2,1}\) proximal operator.
L21_plus_L1([sigma, rho])	L21 + L1 norm proximal operator.
Orthogonal(f, Q[, partial, b, alpha])	Proximal operator of any function of the product between an orthogonal matrix and a vector (plus summation of a vector).
Quadratic([Op, b, c, niter, x0, warm])	Quadratic function proximal operator.
Simplex(n, radius[, dims, axis, maxiter, ...])	Simplex proximal operator.
TV(dims[, sigma, niter, rtol])	TV Norm proximal operator.

Non-Convex

ETP(sigma[, gamma])	Exponential-type penalty (ETP).
Geman(sigma[, gamma])	Geman penalty.
Log(sigma[, gamma])	Logarithmic penalty.
Log1(sigma[, delta])	Logarithmic penalty 2.
QuadraticEnvelopeCard(mu)	Quadratic envelope of the \(\ell_0\)-penalty.
QuadraticEnvelopeCardIndicator(r0)	Quadratic envelope of the indicator function of the \(\ell_0\)-penalty.
RelaxedMumfordShah([sigma, kappa])	Relaxed Mumford-Shah norm proximal operator.
SCAD(sigma[, a])	Smoothly clipped absolute deviation (SCAD) penalty.

Matrix-only

Nuclear(dim[, sigma])	Nuclear norm proximal operator.
NuclearBall(dims, radius[, maxiter, xtol])	Nuclear ball proximal operator.
SingularValuePenalty(dim, penalty)	Proximal operator of a penalty acting on the singular values.
QuadraticEnvelopeRankL2(dim, r0, M)	Quadratic envelope of the rank function with an L2 misfit term.

Other

Nonlinear(x0[, niter, warm])	Nonlinear function proximal operator.
VStack(ops[, nn, restr])	Vertical stacking.

Other operators

BilinearOperator()	Common interface for bilinear operator of a function.
LowRankFactorizedMatrix(X, Y, d[, Op])	Low-Rank Factorized Matrix operator.

Solvers

Primal

AcceleratedProximalGradient(proxf, proxg, x0)	Accelerated Proximal gradient
ADMM(proxf, proxg, x0, tau[, niter, gfirst, ...])	Alternating Direction Method of Multipliers
ADMML2(proxg, Op, b, A, x0, tau[, niter, ...])	Alternating Direction Method of Multipliers for L2 misfit term
GeneralizedProximalGradient(proxfs, proxgs, ...)	Generalized Proximal gradient
HQS(proxf, proxg, x0, tau[, niter, z0, ...])	Half Quadratic splitting
LinearizedADMM(proxf, proxg, A, x0, tau, mu)	Linearized Alternating Direction Method of Multipliers
ProximalGradient(proxf, proxg, x0[, epsg, ...])	Proximal gradient (optionally accelerated)
ProximalPoint(prox, x0, tau[, niter, ...])	Proximal point algorithm
TwIST(proxg, A, b, x0[, alpha, beta, eigs, ...])	Two-step Iterative Shrinkage/Threshold

PALM(H, proxf, proxg, x0, y0[, gammaf, ...])

Proximal Alternating Linearized Minimization

PlugAndPlay(proxf, denoiser, dims, x0[, solver])

Plug-and-Play Priors with any proximal algorithm of choice

SR3(Op, Reg, data, kappa, eps[, x0, ...])

Sparse Relaxed Regularized Regression

Primal-dual

AdaptivePrimalDual(proxf, proxg, A, x0, tau, mu)	Adaptive Primal-dual algorithm
PrimalDual(proxf, proxg, A, x0, tau, mu[, ...])	Primal-dual algorithm

Other

Bregman(proxf, proxg, x0, solver[, A, ...])

Bregman iterations with Proximal Solver

Segment(y, cl, sigma, alpha[, clsigmas, z, ...])

Primal-dual algorithm for image segmentation