abstract type AbstractBoundLoc

Abstract supertype indicating the type of value returned at a specific index.

abstract type AbstractDERelaxIntegrator

Abstract supertype for any integrator that constructs relaxations of a differential equation problem.

abstract type AbstractDERelaxProblem

Abstract supertype for all relaxation problems.

abstract type AbstractDynamicIndex

An abstract supertype for index structures needed to reference parameters or time.

abstract type AbstractIntegratorAttribute

Abstract supertype for attributes that can be used to set or get attributes (properties) of variables in the model.

abstract type AbstractODERelaxIntegrator <: AbstractDERelaxIntegrator

Abstract supertype for any integrator that constructs relaxations of an ordinary differential equation problem.

AbstractODERelaxProblem

Abstract type for problems used to construct relaxations of parametric ODEs.

abstract type AbstractPathConstraint <: AbstractRelaxProblemAttribute

An abstract supertype for all manners of path constraints.

abstract type AbstractRelaxProblemAttribute

Abstract supertype for all problem attributes.

struct AttachedProblem <: AbstractIntegratorAttribute

Retreives the problem used by the integrator.

struct Bound{T<:AbstractBoundLoc} <: AbstractIntegratorAttribute

An integrator attribute for state bounds.

Bound{T}(x::Float64)

This constructor builds a structure that references the state bounds at time = x.

Bound{T}(i::TimeIndex)

This constructor builds a structure that references the state bounds at time index i.

struct ConstantParameterValue <: AbstractIntegratorAttribute

A integrator attribute used to access the constant parameter values.

struct ConstantStateBounds <: AbstractRelaxProblemAttribute

A problem attribute used to store constant state bounds.

• xL::Vector{Float64}

  Lower state variable bounds

• xU::Vector{Float64}

  Upper state variable bounds

struct Gradient{T<:AbstractBoundLoc} <: AbstractIntegratorAttribute

An integrator attribute for the Gradient.

Gradient{T}(x::Float64) where {T <: AbstractBoundLoc}

This constructor builds a structure that references the subgradient of the relaxation at time = x.

Gradient{T}(i::TimeIndex) where {T <: AbstractBoundLoc}

This constructor builds a structure that references the gradient of the relaxation at time index i.

struct HasConstantStateBounds <: AbstractRelaxProblemAttribute

A problem attribute used to check whether state bounds are defined as constant.

struct HasStateBounds <: AbstractRelaxProblemAttribute

A problem attribute used to check whether state bounds are defined.

struct HasUserJacobian <: AbstractRelaxProblemAttribute

A problem attribute used to check whether a user-defined jacobian was specified.

struct HasVariableStateBounds <: AbstractRelaxProblemAttribute

A problem attribute used to check whether variable state bounds are defined.

struct IntegratorName <: AbstractIntegratorAttribute

An integrator attribute for the string identifying the integration scheme.

mutable struct IntegratorStates

A structure that holds the state of the integrator.

• first_pnt_eval::Bool

  Has the first point been evaluated

• new_decision_box::Bool

  Have the box-constraints changed since the last evaluation

• new_decision_pnt::Bool

  Has the decision point changed since the last evaluation

• set_lower_state::Bool

  The relaxed problem has been updated

• set_upper_state::Bool

  The local problem has been updated

• termination_status::TerminationStatusCode

  How did the integrator terminate

struct IsNumeric <: AbstractIntegratorAttribute

An integrator attribute for indicating bounds/relaxations are of numeric solution.

struct IsSolutionSet <: AbstractIntegratorAttribute

An integrator attribute for indicating bounds & relaxations are of exact solution.

struct LocalIntegrator <: AbstractIntegratorAttribute

Retreives the LocalIntegrator that corresponds to the integration method used by the integrator.

struct LocalSensitivityOn <: AbstractIntegratorAttribute

Set to true if integrator should compute derivatives wrt p for the local ode integration.

struct Lower <: AbstractBoundLoc

Indicates the lower bound, relaxation, or (sub)gradient should be returned.

struct Nominal <: AbstractBoundLoc

Indicates the nominal value or (sub)gradient should be returned.

NotAllowedError <: Exception

Abstract type for error thrown when an operation is supported but cannot be applied in the current state of the integrator .

mutable struct ODERelaxProb{F, JX, JP, xType, K} <: AbstractODERelaxProblem

A structure used to hold a parametric ODEs problem.

• f::Any

  Right-hand side function.

• Jx!::Any

  Jacobian of rhs w.r.t x.

• Jp!::Any

  Jacobian of rhs w.r.t p.

• x0::Any

  Initial condition function.

• xL::Vector{Float64}

  Lower constant state bound storage.

• xU::Vector{Float64}

  Upper constant state bound storage.

• tspan::Tuple{Float64, Float64}

  Time span of integration.

• tsupports::Vector{Float64}

  Support points: Points 'x' values will be queried.

• p::Vector{Float64}

  Point to relax/bound in over the decision space.

• pL::Vector{Float64}

  Lower bounds of the decision space.

• pU::Vector{Float64}

  Upper bounds of the decision space.

• user_Jx::Bool

  Problem has a user-defined Jacobian of the rhs w.r.t x

• user_Jp::Bool

  Problem has a user-defined Jacobian of the rhs w.r.t p

• user_state_bnd::Bool

  Constant user state bounds have been set

• variable_state_bnd::Bool

  Variable user state bounds have been set

• nx::Int64

  State space dimension

• np::Int64

  Decision space dimension

• params::Vector{Float64}

  Optional keywork argument: Indicates the rhs function and the initial condition function take an additional argument param. For example, it is now f!(dx, x, p, param).

• polyhedral_constraint::Union{Nothing, PolyhedralConstraint}

  Storage for polyhedral constraint, if any

• constant_state_bounds::Union{Nothing, ConstantStateBounds}

  Storage for the constant state bounds, if any

• support_set::SupportSet{Float64}

  The support set if used

• kwargs::Any

  Additional keyword arguments

ODERelaxProb(f, tspan, x0, pL, pU; kwargs...)

Constructor for basic parametric ODE problem. The f is rhs function. The integration time span is tspan. The initial condition (which may be a function of p) is x0. The lower decision variable bounds are given by pL and the upper decision variable bounds are given by pU. Other inputs are set via keyword arguments.

struct ParameterBound{T<:AbstractBoundLoc} <: AbstractIntegratorAttribute

A integrator attribute used to access the current parameter value.

struct ParameterNumber

An integrator attribute retrieving the number of parameter variables (p) aka np.

struct ParameterValue <: AbstractIntegratorAttribute

A integrator attribute used to access the current parameter value.

struct PolyhedralConstraint <: DynamicBoundsBase.AbstractPathConstraint

An object used to specify that the invariant Ax(t,p) <= b is valid fo all t.

struct Relaxation{T<:AbstractBoundLoc} <: AbstractIntegratorAttribute

An integrator attribute for relaxations.

Relaxation{T}(x::Float64)

This constructor builds a structure that references relaxation at time = x.

Relaxation{T}(i::TimeIndex)

This constructor builds a structure that references the relaxation at time index i.

struct SetRelaxAttributeNotAllowed{AttrType<:Union{AbstractIntegratorAttribute, AbstractRelaxProblemAttribute}} <: DynamicBoundsBase.NotAllowedError

An error indicating that the attribute attr is supported but cannot be set for some reason given in the error string.

struct StateNumber

An integrator attribute retrieving the number of state variables (x) aka nx.

struct Subgradient{T<:AbstractBoundLoc} <: AbstractIntegratorAttribute

An integrator attribute for the Subgradient.

Subgradient{T}(x::Float64)

This constructor builds a structure that references the subgradient of the relaxation at time = x.

Subgradient{T}(i::TimeIndex)

This constructor builds a structure that references the subgradient of the relaxation at time index i.

struct SupportNumber

An integrator attribute retrieving the number of points in the support set of (x) aka nt.

struct SupportSet{T<:AbstractFloat} <: AbstractIntegratorAttribute

A integrator attribute used to access independent variable support set.

struct TerminationStatus <: AbstractIntegratorAttribute

A integrator attribute used to query the TerminationStatusCode of the integrator on completion. Current termination status codes are:

• COMPLETED: The algorithm terminate successfully with bounds and relaxations.
• EMPTY: The algorithm terminated successfully but the solution set was empty for some points in tspan.
• NAN: The algorithm terminated but some values are not a number (usually indicating a domain violation was encoutered when computing relaxations).
• RELAXATION_NOT_CALLED: The relaxation has not yet been computed.
• NUMERICAL_ERROR: A numerical error was encountered.
• LIMIT_EXCEEDED: A preset limit was exceeded (number of steps and so on).
• INVALID_OPTION: An invalid option was set.
• OTHER_ERROR: Another error was encountered.

struct TimeIndex

A time index t used to access the value at t.i-th time point.

struct Undefined <: AbstractBoundLoc

The variety of the attribute is unspecified.

UnsupportedError <: Exception

Abstract type for error thrown when an element is not supported by the integrator.

struct UnsupportedRelaxAttribute{AttrType<:Union{AbstractIntegratorAttribute, AbstractRelaxProblemAttribute}} <: DynamicBoundsBase.UnsupportedError

An error indicating that the attribute attr is unsupported.

struct Upper <: AbstractBoundLoc

Indicates the upper bound, relaxation, or (sub)gradient should be returned.

struct Value <: AbstractIntegratorAttribute

An integrator attribute for value of local solution bounds.

struct VariableStateBounds{F1<:Function, F2<:Function} <: AbstractRelaxProblemAttribute

A problem attribute used to store time-varying state bounds.

• xL::Function

  Lower state variable bounds

• xU::Function

  Upper state variable bounds

get

Returns the value of attribute set for the ::Union{AbstractDERelaxIntegrator, AbstractDERelaxProblem}. May be vector valued.

getall

An version of get which retreives all data asssociated with a particular integrator attribute.

getall!

An in-place version of get! which retreives all data asssociated with a particular integrator attribute.

integrate!

Provides a real-value integration at the current value set for each parameter.

relax!

Computes the relaxation at the current parameter value with the current parameter and state bounds.

set!

Assigns a value to the attr attribute of the integrator, problem, or relaxation.

setall!

An in-place version of set! which sets all data asssociated with a particular integrator attribute.

supports

Return a Bool indicating whether ::AbstractDERelaxIntegrator supports the ::Union{AbstractDERelaxIntegrator, AbstractDERelaxProblem}.