Progressive-hedging solvers

ProgressiveHedgingAlgorithm

Functor object for the progressive-hedging algorithm. Create using the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

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Parameters

• τ::AbstractFloat = 1e-6: Relative tolerance for convergence checks.
• log::Bool = true: Specifices if progressive-hedging procedure should be logged on standard output or not.

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AbstractProgressiveHedgingAttribute

Abstract supertype for attribute objects specific to the progressive-hedging algorithm.

DualTolerance

An optimizer attribute for specifying the dual tolerance in the progressive-hedging algorithm.

PenalizationParameter

Abstract supertype for penalization-specific attributes.

Regularizer

An optimizer attribute for specifying a penalization procedure to be used in the progressive-hedging algorithm. Options are:

• Fixed: Fixed penalty (default) ?Fixed for parameter descriptions.
• Adaptive: Adaptive penalty update ?Adaptive for parameter descriptions.

Penaltyterm

An optimizer attribute for specifying what proximal term should be used in subproblemsof the progressive-hedging algorithm. Options are:

• Quadratic (default)
• Linearized
• InfNorm
• ManhattanNorm

PrimalTolerance

An optimizer attribute for specifying the primal tolerance in the progressive-hedging algorithm.

Optimizer(; <keyword arguments>)

Return a progressive-hedging optimizer.

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Arguments

• subproblem_optimizer::AbstractOptimizer: MathOptInterface solver capable of solving quadratic programs.
• penalty::AbstractPenalizer = Fixed(): Specify penalty update procedure (Fixed, Adaptive)
• execution::AbstractExecuter = Serial: Specify how algorithm should be executed (Serial, Synchronous, Asynchronous). Distributed variants requires worker cores.
• penaltyterm::PenaltyTerm = Quadratic: Specify penaltyterm variant (Quadratic, Linearized, InfNorm, [ManhattanNorm][@ref])
• <keyword arguments>: Algorithm specific parameters, consult individual docstrings (see above list) for list of possible arguments and default values.

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get_penalization_attribute(stochasticprogram::StochasticProgram, name::String)

Return the value associated with the penalization-specific attribute named name in stochasticprogram.

See also: set_penalization_attribute, set_penalization_attributes.

set_penalization_attribute(stochasticprogram::StochasticProgram, name::Union{Symbol, String}, value)

Sets the penalization-specific attribute identified by name to value.

set_penalization_attributes(stochasticprogram::StochasticProgram, pairs::Pair...)

Given a list of attribute => value pairs or a collection of keyword arguments, calls set_penalization_attribute(stochasticprogram, attribute, value) for each pair.

SerialExecution

Functor object for using serial execution in a progressive-hedging algorithm. Create by supplying a Serial object through execution in the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

SynchronousExecution

Functor object for using synchronous execution in a progressive-hedging algorithm (assuming multiple Julia cores are available). Create by supplying a Synchronous object through execution in the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

AsynchronousExecution

Functor object for using asynchronous execution in a progressive-hedging algorithm (assuming multiple Julia cores are available). Create by supplying an Asynchronous object through execution in the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

set_penalization_attribute(stochasticprogram::StochasticProgram, name::Union{Symbol, String}, value)

Sets the penalization-specific attribute identified by name to value.

set_penalization_attributes(stochasticprogram::StochasticProgram, pairs::Pair...)

Given a list of attribute => value pairs or a collection of keyword arguments, calls set_penalization_attribute(stochasticprogram, attribute, value) for each pair.

RawPenalizationParameter

An optimizer attribute used for raw parameters of the penalizer. Defers to RawParameter.

FixedPenalization

Functor object for using fixed penalty in a progressive-hedging algorithm. Create by supplying a Fixed object through penalty in the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

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Parameters

• r::T = 1.00: Fixed penalty

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Fixed

Factory object for FixedPenalization. Pass to penalty in the ProgressiveHedgingSolver factory function. See ?FixedPenalization for parameter descriptions.

AdaptivePenalization

Functor object for using adaptive penalty in a progressive-hedging algorithm. Create by supplying an Adaptive object through penalty in the ProgressiveHedgingSolver factory function and then pass to a StochasticPrograms.jl model.

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Parameters

• ζ::T = 0.1: Used to calculate the initial penalty. Non-anticipativity in the initial decision is enforced more as ζ increase.
• γ₁::T = 1e-5: Tolerance for primal changes being significant
• γ₂::T = 0.01: Tolerance for primal changes dominating dual changes
• γ₃::T = 0.25: Tolerance for dual changes dominating primal changes
• σ::T = 1e-5: Tolerance for the quadratic penalty dominating the Lagrangian
• α::T = 0.95: Penalty decrease after primal changes dominating dual changes
• θ::T = 1.1: Penalty increase after dual changes dominating primal changes
• ν::T = 0.1: Tolerance for significant non-anticipativity violation
• β::T = 1.1: Penalty increase after increased non-anticipativity violation
• η::T = 1.25: Default penalty increase in the default case

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Adaptive

Factory object for AdaptivePenalization. Pass to penalty in the ProgressiveHedgingSolver factory function. See ?AdaptivePenalization for parameter descriptions.