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Internals

These symbols are not part of the public API, their behavior may change without warning between releases.

CoolPDLP.ConstraintMatrix — Type
ConstraintMatrix

Fields

  • A::SparseArrays.AbstractSparseMatrix{T, Ti} where {T<:Number, Ti<:Integer}

  • At::SparseArrays.AbstractSparseMatrix{T, Ti} where {T<:Number, Ti<:Integer}

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CoolPDLP.ConvergenceStats — Type
ConvergenceStats

Fields

  • err::CoolPDLP.KKTErrors: current KKT error

  • starting_time::Float64: time at which the algorithm started, in seconds

  • time_elapsed::Float64: time elapsed since the algorithm started, in seconds

  • kkt_passes::Int64: number of multiplications by both the KKT matrix and its transpose

  • termination_status::CoolPDLP.TerminationStatus: termination stats (should be STILL_RUNNING until the algorithm actually terminates)

  • error_history::Array{Tuple{Int64, CoolPDLP.KKTErrors{T}}, 1} where T<:Number

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CoolPDLP.ConversionParameters — Type
ConversionParameters{T,Ti,M}

Type parameters

  • T: floating point type to convert values to
  • Ti: integer type to convert indices to
  • M: matrix constructor to use on the constraints

Fields

  • backend::KernelAbstractions.Backend: CPU or GPU backend used for computations
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CoolPDLP.GenericParameters — Type
GenericParameters

Fields

  • show_progress::Bool: whether to show a progress bar

  • check_every::Int64: frequency of restart or termination checks

  • record_error_history::Bool: whether or not to record error evolution

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CoolPDLP.KKTErrors — Type
KKTErrors

Fields

  • primal::Number: primal feasibility error

  • primal_scale::Number: characteristic scale of the primal constraint RHS

  • dual::Number: dual feasibility error

  • dual_scale::Number: characteristic scale of the dual constraint RHS

  • gap::Number: primal-dual gap

  • gap_scale::Number: characteristic scale of the gap

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CoolPDLP.PDHGState — Type
PDHGState

Fields

  • sol::PrimalDualSolution: current solution

  • sol_last::PrimalDualSolution: last solution

  • step_sizes::CoolPDLP.StepSizes: step sizes

  • scratch::CoolPDLP.Scratch: scratch space

  • stats::CoolPDLP.ConvergenceStats: convergence stats

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CoolPDLP.PDLPState — Type
PDHGState

Fields

  • sol::PrimalDualSolution: current solution

  • sol_last::PrimalDualSolution: last solution

  • sol_avg::PrimalDualSolution: current average solution

  • sol_avg_last::PrimalDualSolution: last average solution

  • sol_restart::PrimalDualSolution: solution from last restart

  • step_sizes::CoolPDLP.StepSizes: step sizes

  • scratch::CoolPDLP.Scratch: scratch space

  • iteration::CoolPDLP.IterationCounter: iteration counter

  • restart_stats::CoolPDLP.RestartStats: restart stats

  • stats::CoolPDLP.ConvergenceStats: convergence stats

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CoolPDLP.Preconditioner — Type
Preconditioner

Fields

  • D1::LinearAlgebra.Diagonal{T, V} where {T<:Number, V<:DenseVector{T}}: left preconditioner

  • D2::LinearAlgebra.Diagonal{T, V} where {T<:Number, V<:DenseVector{T}}: right preconditioner

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CoolPDLP.PreconditioningParameters — Type
PreconditioningParameters

Fields

  • chambolle_pock_alpha::Any: norm parameter in the Chambolle-pock preconditioner

  • ruiz_iter::Int64: iteration parameter in the Ruiz preconditioner

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CoolPDLP.RestartParameters — Type
RestartParameters

Fields

  • sufficient_decay::Number: restart criterion: sufficient decay in normalized duality gap

  • necessary_decay::Number: restart criterion: necessary decay

  • artificial_decay::Number: restart criterion: long inner loop

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CoolPDLP.RestartStats — Type
RestartStats

Fields

  • restart_from_avg::Bool

  • err_candidate::CoolPDLP.KKTErrors

  • err_candidate_last::CoolPDLP.KKTErrors

  • err_restart::CoolPDLP.KKTErrors

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CoolPDLP.StepSizeParameters — Type
StepSizeParameters

Fields

  • invnorm_scaling::Number: scaling of the inverse spectral norm of A when defining the non-adaptive step size

  • primal_weight_damping::Number: primal weight update damping

  • zero_tol::Number: tolerance in absolute comparisons to zero

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CoolPDLP.StepSizes — Type
StepSizes

Fields

  • η::Number: step size

  • η_sum::Number: cumulated step size since last restart

  • ω::Number: primal weight

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CoolPDLP.TerminationParameters — Type
TerminationParameters

Fields

  • termination_reltol::Number: tolerance on KKT relative errors to decide termination

  • max_kkt_passes::Int64: maximum number of multiplications by both the KKT matrix K and its transpose Kᵀ

  • time_limit::Float64: time limit in seconds

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CoolPDLP.TerminationStatus — Type
TerminationStatus

Enum for the various ways that an algorithm can terminate.

Possible values:

  • OPTIMAL
  • TIME_LIMIT
  • ITERATION_LIMIT
  • STILL_RUNNING
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CoolPDLP.##is_feasible_simulator#433 — Method
is_feasible(x, milp[; cons_tol=1e-6, int_tol=1e-5, verbose=true])

Check whether solution vector x is feasible for milp.

Keyword arguments

  • cons_tol: tolerance for constraint satisfaction
  • int_tol: tolerance for integrality requirements
  • verbose: whether to display warnings
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CoolPDLP.##preprocess_simulator#591 — Method
preprocess(milp_init, sol_init, algo)

Apply preconditioning, type conversion and device transfer to milp_init and sol_init for the algorithm defined by algo.

Return a tuple (milp, sol).

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CoolPDLP.##proj_multiplier_simulator#371 — Method
proj_multiplier(λ, l, u)

Project λ onto the feasible space of the (double) Lagrange multiplier λ⁺ - λ⁻ associated with the constraint l ≤ x ≤ u, where l and/or u might be infinite.

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CoolPDLP.##solve_simulator#595 — Method
solve(milp, sol, algo)
solve(milp, algo)

Solve the continuous relaxation of milp starting from solution sol using the algorithm defined by algo.

Return a couple (sol, stats) where sol is the last solution and stats contains convergence information.

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CoolPDLP.combine — Method
combine(l, u)

Return the largest finite absolute value between the two bounds, or zero if neither is finite.

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CoolPDLP.common_backend — Method
common_backend(args...)

Return the common GPU backend of several arguments, if it exists, and throw an error otherwise.

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CoolPDLP.proj_multiplier — Method
proj_multiplier(λ, l, u)

Project λ onto the feasible space of the (double) Lagrange multiplier λ⁺ - λ⁻ associated with the constraint l ≤ x ≤ u, where l and/or u might be infinite.

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CoolPDLP.set_eltype — Method
set_eltype(T, milp)

Change the element type of floating-point containers inside milp to T.

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CoolPDLP.sort_rows_columns — Method
sort_rows_columns(milp)

Return a new MILP where the constraint matrix has been permuted by order of increasing column and row density.

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