Module convex_analysis 

Convex analysis, proximal operators, and constrained optimisation.

Implements convex sets (hyperplane, halfspace, ball, polytope), projection operators, proximal maps, dual decomposition with subgradient updates, ADMM, Frank-Wolfe / conditional gradient, and the ellipsoid method.

Structs

AdmmResult

Result returned by the ADMM solver.

AdmmSolver

Alternating Direction Method of Multipliers (ADMM) for problems of the form:

DualDecomposition

Lagrangian relaxation with subgradient updates for dual decomposition.

EllipsoidMethod

Ellipsoid method for convex feasibility problems.

EllipsoidResult

Result from the ellipsoid method.

FrankWolfeOptimizer

Frank-Wolfe (conditional gradient) method for constrained convex problems.

FrankWolfeResult

Result from the Frank-Wolfe algorithm.

MorseEnvelope

Moreau envelope (inf-convolution) smoothing of a convex function.

ProjectionOperator

Collection of projection operators onto standard convex sets.

ProximalOperator

A proximal operator parameterised by a regularisation strength lambda.

SubgradientMethod

Configuration for subgradient descent.

SupportFunction

Support function of a convex polygon given by its vertices in ℝ².

Enums

ConvexSet

A representation of a convex set in ℝⁿ.

Functions

conjugate_function_1d

Compute the Legendre–Fenchel conjugate f*(y) = sup_{x ∈ domain} (y·x - f(x)) via a grid search over n equally-spaced points on domain = (lo, hi).

dykstra_projection

Project x onto the intersection of convex sets using Dykstra’s algorithm.

is_convex_1d

Check whether a discretely sampled 1-D function is (approximately) convex.

moreau_envelope_l1

Moreau envelope of the L1 norm: smooth approximation to |x|.

proj_box

Project x onto the axis-aligned box [lo, hi] component-wise.

proj_simplex

Project x onto the probability simplex Δ = {z ≥ 0 : sum z = 1}.

prox_huber

Proximal operator of the Huber loss with parameter delta.

prox_l1

Soft-thresholding (proximal operator of the L1 norm): prox_{λ|·|}(x).

prox_l2_sq

Proximal operator of the squared L2 norm (ridge): x / (1 + λ).

subgradient_descent

Run iters steps of subgradient descent on grad_f from x0 with step size lr.