Repo Organization

• benchmark: scripts used to measure characteristics of our algorithms on different problems
• data: example data sets for problems (mainly convex clustering)
• demo: smaller scripts demonstrating proximal distance methods on different problems
• test: test scripts, mainly linear operators and projections
• src: source code

Driver code

• acceleration.jl: Implements Nesterov acceleration. These are generic and designed to work for any problem and solver in this repo.

• common.jl: Provides various utilities used interally. Also defines an interface for callbacks, passed using the callback keyword argument, that can be used to record, plot, or otherwise display convergence histories.

• linsolve.jl: Provides wrappers for LSMR, LSQR, and CG from IterativeSolvers.jl.

• optimize.jl: Implements optimize! and anneal!, functions that handle the logic of proximal distance iteration, checking convergence, and logging. Also defines the ProxDistProblem used internally.

• projections.jl: Defines types for doing projections internally.

• ProximalDistanceAlgorithms.jl: Importing and exporting; mostly importing. Defines algorithm types passed to solvers (e.g. MM() for MM option).

Problem-specific code is isolated in its own folder within src: condition_number, convex_clustering, convex_regression, image_denoising, and metric_nearness. Each of these subfolders contains the files

operators.jl: This file implements the problem's fusion matrix D <: FusionMatrix as a linear map. These types are fully compatible with +, *, transpose, and other linear algebra information. These should optimize for matrix-vector multiplication. In most cases, there is a DtD <: FusionGramMatrix operator to handle y = D'D*x efficiently (there is no need to construct it explicity).

implementation.jl: Defines an interface that constructs a ProxDistProblem that is passed to optimize!, the problem's optimization model, and algorithm maps for each solver. Algorithm maps should share the same function name but specialize on the solver option, e.g. to define the map for SteepestDescent we write

function problem_algmap(::SteepestDescent, prob, ρ, μ)
    # implementation details
    return stepsize
end

These functions should also return a stepsize that is recorded elsewhere. Use the convention stepsize = 1.0 as a default.