### Include Example Scripts

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

Includes necessary example scripts for plotting and linear regression after activating the test environment.

```julia
include("examples/plot_utils.jl")
include("examples/linear_regression.jl")
...
```

--------------------------------

### Add FrankWolfe.jl (Master Branch)

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

Install the master branch of the FrankWolfe.jl package directly from its GitHub repository.

```julia
Pkg.add(url="https://github.com/ZIB-IOL/FrankWolfe.jl", rev="master")
```

--------------------------------

### Include Plotting Utilities in Your Project

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

Includes the plotting utilities from the FrankWolfe.jl examples directory into your current project. Ensure Plots.jl is already included in your project.

```julia
using Plots
using FrankWolfe

include(joinpath(dirname(pathof(FrankWolfe)), "../examples/plot_utils.jl"))
```

--------------------------------

### Add FrankWolfe.jl (Latest Release)

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

Install the most recent release of the FrankWolfe.jl package using the Julia package manager.

```julia
using Pkg
Pkg.add("FrankWolfe")
```

--------------------------------

### Solving a Quadratic Minimization Problem on the Probability Simplex

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

This snippet shows a minimal example of using the `frank_wolfe` function to solve a quadratic objective function on the probability simplex. It requires defining the objective function, its gradient, a linear minimization oracle, and a starting vector.

```julia
using FrankWolfe

# objective function f(p) = p_1^2 + ... + p_n^2
f(p) = sum(abs2, p)

# in-place gradient computation for f thanks to '.='
grad!(storage, p) = storage .= 2p  

# pre-defined type implementing the linear minimization oracle interface for the simplex
lmo = FrankWolfe.ProbabilitySimplexLMO(1.)

# starting vector (of dimension n=3)
p0 = [1., 0., 0.]

# an optimal solution is returned in p_opt
p_opt, _ = frank_wolfe(f, grad!, lmo, p0; verbose=true);
```

```julia
p_opt
```

--------------------------------

### Activate Test Environment with TestEnv.jl

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/README.md

Activates the test environment for the FrankWolfe.jl package. This is a prerequisite for running the provided examples.

```julia
using TestEnv

TestEnv.activate()
"/tmp/jl_Ux8wKE/Project.toml"
```

--------------------------------

### Frank-Wolfe Algorithm Output

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This output shows the performance of the Vanilla Frank-Wolfe Algorithm on a large-scale problem. It details iteration count, primal and dual objective values, dual gap, and time, illustrating memory-agnostic convergence.

```text
Vanilla Frank-Wolfe Algorithm.
EMPHASIS: memory STEPSIZE: agnostic EPSILON: 1.0e-7 MAXITERATION: 1000 TYPE: Float64
MOMENTUM: nothing GRADIENT_TYPE: Nothing

─────────────────────────────────────────────────────────────────────────────────────────────────
  Type     Iteration         Primal           Dual       Dual Gap           Time         It/sec
─────────────────────────────────────────────────────────────────────────────────────────────────
     I             0   1.000000e+00  -1.000000e+00   2.000000e+00   8.783523e+00   0.000000e+00
    FW           100   1.326732e-02  -1.326733e-02   2.653465e-02   4.635923e+02   2.157068e-01
    FW           200   6.650080e-03  -6.650086e-03   1.330017e-02   9.181294e+02   2.178342e-01
    FW           300   4.437059e-03  -4.437064e-03   8.874123e-03   1.372615e+03   2.185609e-01
    FW           400   3.329174e-03  -3.329180e-03   6.658354e-03   1.827260e+03   2.189070e-01
    FW           500   2.664003e-03  -2.664008e-03   5.328011e-03   2.281865e+03   2.191190e-01
    FW           600   2.220371e-03  -2.220376e-03   4.440747e-03   2.736387e+03   2.192672e-01
    FW           700   1.903401e-03  -1.903406e-03   3.806807e-03   3.190951e+03   2.193703e-01
    FW           800   1.665624e-03  -1.665629e-03   3.331253e-03   3.645425e+03   2.194532e-01
    FW           900   1.480657e-03  -1.480662e-03   2.961319e-03   4.099931e+03   2.195159e-01
    FW          1000   1.332665e-03  -1.332670e-03   2.665335e-03   4.554703e+03   2.195533e-01
  Last          1000   1.331334e-03  -1.331339e-03   2.662673e-03   4.559822e+03   2.195261e-01
─────────────────────────────────────────────────────────────────────────────────────────────────

4560.661203 seconds (7.41 M allocations: 112.121 GiB, 0.01% gc time)
```

--------------------------------

### Frank-Wolfe Algorithm with Rational Arithmetic Output

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This output shows the convergence of the Vanilla Frank-Wolfe Algorithm using rational arithmetic for the approximate Carathéodory problem. It highlights the precision of the solution obtained.

```text
Vanilla Frank-Wolfe Algorithm.
EMPHASIS: blas STEPSIZE: rationalshortstep EPSILON: 1.0e-7 max_iteration: 100 TYPE: Rational{BigInt}

───────────────────────────────────────────────────────────────────────────────────
  Type     Iteration         Primal           Dual       Dual Gap           Time
───────────────────────────────────────────────────────────────────────────────────
     I             0   1.000000e+00  -1.000000e+00   2.000000e+00   1.540385e-01
    FW            10   9.090909e-02  -9.090909e-02   1.818182e-01   2.821186e-01
    FW            20   4.761905e-02  -4.761905e-02   9.523810e-02   3.027964e-01
    FW            30   3.225806e-02  -3.225806e-02   6.451613e-02   3.100331e-01
    FW            40   2.439024e-02  -2.439024e-02   4.878049e-02   3.171654e-01
    FW            50   1.960784e-02  -1.960784e-02   3.921569e-02   3.244207e-01
    FW            60   1.639344e-02  -1.639344e-02   3.278689e-02   3.326185e-01
    FW            70   1.408451e-02  -1.408451e-02   2.816901e-02   3.418239e-01
    FW            80   1.234568e-02  -1.234568e-02   2.469136e-02   3.518750e-01
    FW            90   1.098901e-02  -1.098901e-02   2.197802e-02   3.620287e-01
  Last                 1.000000e-02   1.000000e-02   0.000000e+00   4.392171e-01
───────────────────────────────────────────────────────────────────────────────────

  0.600608 seconds (3.83 M allocations: 111.274 MiB, 12.97% gc time) 

Output type of solution: Rational{BigInt}

```

--------------------------------

### FrankWolfe Utils Module Documentation

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the utility functions module for FrankWolfe.jl.

```julia
Modules = [FrankWolfe]
Pages = ["utils.jl"]
```

--------------------------------

### FrankWolfe Index Documentation

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Provides an index for the FrankWolfe.jl documentation, specifically referencing the 3_backend.md page.

```julia
Pages = ["3_backend.md"]
```

--------------------------------

### Autodocs for Gradient Descent Module

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/5_gradient_descent.md

This snippet generates documentation for the gradient descent module within the FrankWolfe.jl package.

```julia
```@autodocs
Modules = [FrankWolfe.Experimental]
Pages = ["gradient_descent.jl"]
```
```

--------------------------------

### Meta-LMO Wrappers

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/2_lmo.md

Provides wrappers for LMOs to extend their behavior, such as caching.

```julia
FrankWolfe.CachedLMO
```

```julia
FrankWolfe.ProductLMO
```

```julia
FrankWolfe.SingleLastCachedLMO
```

```julia
FrankWolfe.MultiCacheLMO
```

```julia
FrankWolfe.VectorCacheLMO
```

--------------------------------

### Autodocs for Line Search Module

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/4_linesearch.md

Generates documentation for the FrankWolfe linesearch.jl module, including types and functions related to line search.

```julia
```@autodocs
Modules = [FrankWolfe]
Pages = ["linesearch.jl"]
```
```

--------------------------------

### Keyword Arguments for Extra Vertex Storage

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

Pass these keyword arguments to Frank-Wolfe algorithms that use an active set to enable and configure extra vertex storage. This can help in managing discarded vertices and utilizing stored vertices.

```julia
add_dropped_vertices=true,
use_extra_vertex_storage=true,
extra_vertex_storage=vertex_storage,
```

--------------------------------

### Benchmarking Large-scale Problem Solvers

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This output details the performance benchmarking of different components (f, grad, lmo, dual gap, update) for large-scale problems. It compares the standard BLAS update with the memory-efficient 'memory' emphasis mode, showing significant differences in time and memory allocations.

```text
Size of single vector (Float64): 7629.39453125 MB
Testing f... 100%|█████████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:23
Testing grad... 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:23
Testing lmo... 100%|███████████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:29
Testing dual gap... 100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:46
Testing update... (Emphasis: blas) 100%|███████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:01:35
Testing update... (Emphasis: memory) 100%|█████████████████████████████████████████████████████████████████████████████████████████████| Time: 0:00:58
 ──────────────────────────────────────────────────────────────────────────
                                   Time                   Allocations
                           ──────────────────────   ───────────────────────
     Tot / % measured:           278s / 31.4%            969GiB / 30.8%

 Section           ncalls     time   %tot     avg     alloc   %tot      avg
 ──────────────────────────────────────────────────────────────────────────
 update (blas)         10    36.1s  41.3%   3.61s    149GiB  50.0%  14.9GiB
 lmo                   10    18.4s  21.1%   1.84s     0.00B  0.00%    0.00B
 grad                  10    12.8s  14.6%   1.28s   74.5GiB  25.0%  7.45GiB
 f                     10    12.7s  14.5%   1.27s   74.5GiB  25.0%  7.45GiB
 update (memory)       10    5.00s  5.72%   500ms     0.00B  0.00%    0.00B
 dual gap              10    2.40s  2.75%   240ms     0.00B  0.00%    0.00B
 ──────────────────────────────────────────────────────────────────────────
```

--------------------------------

### FrankWolfe Active Set Modules

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the modules related to active set management in FrankWolfe.jl.

```julia
Modules = [FrankWolfe]
Pages = ["active_set.jl", "active_set_quadratic.jl", "active_set_quadratic_direct_solve.jl", "active_set_sparsifier.jl"]
```

--------------------------------

### Define a Custom Linear Minimization Oracle

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/basics.md

To use a custom LMO, it must be a subtype of FrankWolfe.LinearMinimizationOracle and implement the compute_extreme_point method. The constraint set does not need explicit representation.

```julia
FrankWolfe.compute_extreme_point(lmo::MyLMO, direction; v, kwargs...) -> v
```

--------------------------------

### FrankWolfe Types Module Documentation

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the core types module for FrankWolfe.jl.

```julia
Modules = [FrankWolfe]
Pages = ["types.jl"]
```

--------------------------------

### Perform Line Search Function

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/4_linesearch.md

The core method called at each iteration to compute the step size (gamma). This function is implemented by concrete line search strategies.

```julia
```@docs
FrankWolfe.perform_line_search
```
```

--------------------------------

### FrankWolfe CallbackState Documentation

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the CallbackState type used for callbacks in FrankWolfe.jl.

```julia
FrankWolfe.CallbackState
```

--------------------------------

### FrankWolfe Function Gradient Module

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the module for functions and gradients in FrankWolfe.jl.

```julia
Modules = [FrankWolfe]
Pages = ["function_gradient.jl"]
```

--------------------------------

### Callback Function Signature

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

Define a callback function that accepts a `FrankWolfe.CallbackState` struct and additional arguments. This is useful for logging or storing intermediate algorithm states.

```julia
callback(state::FrankWolfe.CallbackState, args...)

```

--------------------------------

### FrankWolfe Custom Vertex Storage Types

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents custom types for efficient storage and operations on extreme points of feasible sets.

```julia
FrankWolfe.ScaledHotVector
```

```julia
FrankWolfe.RankOneMatrix
```

--------------------------------

### Exact Optimal Solution with Rational Arithmetic

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This output displays the exact optimal solution vector 'x' obtained using rational arithmetic for the approximate Carathéodory problem. Each element of the vector is a rational number.

```julia
x = Rational{BigInt}[1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100, 1//100]

```

--------------------------------

### Compute Extreme Point Method

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/2_lmo.md

The core method implemented by all LMO subtypes to compute an extreme point of the feasible set.

```julia
compute_extreme_point
```

--------------------------------

### Standard Algorithm Signature

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/1_algorithms.md

The typical function signature for standard algorithms in the package. This signature is used across various optimization methods.

```julia
my_algorithm(f, grad!, lmo, x0)
```

--------------------------------

### Documenting a Julia Function

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/CONTRIBUTING.md

Use triple double quotation marks to add documentation comments above Julia functions, supporting Markdown formatting.

```julia
"""
This explains what the function `f` does, it supports markdown.
"""
function f(x)
    # ...
end
```

--------------------------------

### FrankWolfe Oracle Tracking Types

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents wrapper types for oracles that track the number of calls made.

```julia
FrankWolfe.TrackingObjective
```

```julia
FrankWolfe.TrackingGradient
```

```julia
FrankWolfe.TrackingLMO
```

--------------------------------

### FrankWolfe.alternating_linear_minimization

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/1_algorithms.md

Converts a problem over the intersection of convex sets into a series of subproblems over single sets using alternating linear minimization. It aims to find a point within the intersection by minimizing the distance to iterates of other subproblems and the original objective function.

```APIDOC
## FrankWolfe.alternating_linear_minimization

### Description
Converts a problem over the intersection of convex sets into a series of subproblems over single sets using alternating linear minimization. It aims to find a point within the intersection by minimizing the distance to iterates of other subproblems and the original objective function.

### Method Signature
```julia
alternating_linear_minimization(f, grad!, lmos, x0)
```

### Parameters
- **f**: The objective function to minimize.
- **grad!**: A function that computes the gradient of `f`.
- **lmos**: A list of linear minimization oracles, one for each convex set.
- **x0**: The initial point.
```

--------------------------------

### LMO Interface Definition

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/2_lmo.md

Defines the abstract type for Linear Minimization Oracles.

```julia
FrankWolfe.LinearMinimizationOracle
```

--------------------------------

### FrankWolfe.LinearMinimizationOracle

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/2_lmo.md

The abstract type for all Linear Minimization Oracles. It is a key component called at each iteration of the FW algorithm. Given `d` in the feasible set `X`, it returns a vertex `v` of the feasible set that minimizes the dot product \langle d, x \rangle.

```APIDOC
## Type: FrankWolfe.LinearMinimizationOracle

### Description
Abstract type for Linear Minimization Oracles. These oracles are invoked at each iteration of the Frank-Wolfe algorithm to find a vertex of the feasible set that minimizes a linear objective function.

### Subtypes
- `FrankWolfe.CachedLMO`
- `FrankWolfe.ProductLMO`
- `FrankWolfe.SingleLastCachedLMO`
- `FrankWolfe.MultiCacheLMO`
- `FrankWolfe.VectorCacheLMO`
- Oracles defined in `norm_oracles.jl`, `simplex_oracles.jl`, `polytope_oracles.jl`, `spectral_oracles.jl`, and `moi_oracle.jl`.
```

--------------------------------

### FrankWolfe.block_coordinate_frank_wolfe

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/1_algorithms.md

Implements the Block Coordinate Frank-Wolfe algorithm. This method is suitable for problems where the objective function or constraints can be decomposed into blocks.

```APIDOC
## FrankWolfe.block_coordinate_frank_wolfe

### Description
Implements the Block Coordinate Frank-Wolfe algorithm. This method is suitable for problems where the objective function or constraints can be decomposed into blocks.

### Method Signature
```julia
block_coordinate_frank_wolfe(f, grad!, lmo, x0)
```

### Parameters
- **f**: The objective function to minimize.
- **grad!**: A function that computes the gradient of `f`.
- **lmo**: A linear minimization oracle.
- **x0**: The initial point.
```

--------------------------------

### FrankWolfe.alternating_projections

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/1_algorithms.md

Solves feasibility problems over intersections of feasible regions using an alternating projections approach. This method is designed for finding a point that satisfies constraints across multiple sets.

```APIDOC
## FrankWolfe.alternating_projections

### Description
Solves feasibility problems over intersections of feasible regions using an alternating projections approach. This method is designed for finding a point that satisfies constraints across multiple sets.

### Method Signature
```julia
alternating_projections(constraints, x0)
```

### Parameters
- **constraints**: A list of constraints defining the feasible regions.
- **x0**: The initial point.
```

--------------------------------

### FrankWolfe Block-Coordinate Update Step Types

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents subtypes of UpdateStep and the update_block_iterate method for defining iterations in block-coordinate Frank-Wolfe.

```julia
FrankWolfe.UpdateStep
```

```julia
FrankWolfe.update_block_iterate
```

```julia
FrankWolfe.FrankWolfeStep
```

```julia
FrankWolfe.BPCGStep
```

--------------------------------

### Required Methods for Iterate Type

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

These methods must be implemented for iterate types that behave as members of a Hilbert space and are optionally mutable.

```julia
Base.similar(::IT)
Base.similar(::IT, ::Type{T})
Base.collect(::IT)
Base.size(::IT)
Base.eltype(::IT)
Base.copyto!(dest::IT, src::IT)

Base.:+(x1::IT, x2::IT)
Base.:*(scalar::Real, x::IT)
Base.:-(x1::IT, x2::IT)
LinearAlgebra.dot(x1::IT, x2::IT)
LinearAlgebra.norm(::IT)
```

--------------------------------

### FrankWolfe BlockVector Documentation

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents the BlockVector type for representing block vectors in FrankWolfe.jl.

```julia
FrankWolfe.BlockVector
```

--------------------------------

### Active Set Update Methods

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

These methods are used to update the iterate within the active set computation.

```julia
FrankWolfe.active_set_update_scale!(x::IT, lambda, atom)
FrankWolfe.active_set_update_iterate_pairwise!(x::IT, lambda, fw_atom, away_atom)
```

--------------------------------

### FrankWolfe Block Coordinate Update Order Types

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/3_backend.md

Documents subtypes of BlockCoordinateUpdateOrder and the select_update_indices method for controlling block updates.

```julia
FrankWolfe.BlockCoordinateUpdateOrder
```

```julia
FrankWolfe.select_update_indices
```

```julia
FrankWolfe.FullUpdate
```

```julia
FrankWolfe.CyclicUpdate
```

```julia
FrankWolfe.StochasticUpdate
```

```julia
FrankWolfe.LazyUpdate
```

--------------------------------

### Frank-Wolfe Line Search Method Type

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/4_linesearch.md

Defines the abstract type for all line search methods used in Frank-Wolfe algorithms. Implementations must define the `perform_line_search` method.

```julia
```@docs
FrankWolfe.LineSearchMethod
```
```

--------------------------------

### Compute Active Set Iterate

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This method is required if the iterate type is not a broadcastable mutable object. It recomputes the iterate from the convex decomposition.

```julia
FrankWolfe.compute_active_set_iterate!(active_set::FrankWolfe.ActiveSet{AT, R, IT}) where {AT, R}
```

--------------------------------

### compute_extreme_point

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/reference/2_lmo.md

Computes an extreme point of the feasible set given a direction vector. This is the core method implemented by all subtypes of `LinearMinimizationOracle`.

```APIDOC
## Method: compute_extreme_point

### Description
Computes an extreme point of the feasible set given a direction vector `d`. This method is implemented by all subtypes of `FrankWolfe.LinearMinimizationOracle` and is central to the Frank-Wolfe algorithm.

### Signature
```julia
compute_extreme_point(lmo::LinearMinimizationOracle, d::AbstractVector)
```

### Parameters
- `lmo` (LinearMinimizationOracle): The Linear Minimization Oracle instance.
- `d` (AbstractVector): The direction vector in the dual space.

### Returns
An `AbstractVector` representing an extreme point of the feasible set that minimizes \langle d, x \rangle.
```

--------------------------------

### Reynolds Operator Definition

Source: https://github.com/zib-iol/frankwolfe.jl/blob/master/docs/src/advanced.md

This mathematical definition illustrates the Reynolds operator used for symmetry reduction. It averages group actions to find an invariant subspace.

```math
\mathcal{R}(x)=\frac{1}{|G|}\sum_{g\in G}g\cdot x.
```

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