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Add variable bridges
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‎docs/src/apimanual.md‎

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@@ -4,6 +4,7 @@ DocTestSetup = quote
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using MathOptInterface
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const MOI = MathOptInterface
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end
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DocTestFilters = [r"MathOptInterface|MOI"]
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```
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# Manual
@@ -931,20 +932,60 @@ between `y_i` and the vector of scalar-valued quadratic functions.
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### Automatic reformulation
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#### Variable reformulation
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A variable is often created in a set unsupported by the solver while it could be
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parametrized by variables constrained in supported sets.
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For example, the [`Bridges.Variable.VectorizeBridge`](@ref) defines the
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reformulation of a constrained variable in [`GreaterThan`](@ref) into a
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constrained vector of one variable in [`Nonnegatives`](@ref).
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The `Bridges.Variable.Vectorize` is the bridge optimizer that applies the
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[`Bridges.Variable.VectorizeBridge`](@ref) rewritting rule. Given an optimizer
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`optimizer` implementing constrained variables in [`Nonnegatives`](@ref) and,
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the optimizer
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```jldoctest; setup=:(optimizer = MOI.Utilities.Model{Float64}())
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bridged_optimizer = MOI.Bridges.Variable.Vectorize{Float64}(optimizer)
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MOI.supports_constraint(bridged_optimizer, MOI.SingleVariable, MOI.GreaterThan{Float64})
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# output
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true
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```
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will additionally support constrained variables in [`GreaterThan`](@ref).
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Note that these [`Bridges.Variable.SingleBridgeOptimizer`](@ref) are mainly
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used for testing bridges. It is recommended to rather use
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[`Bridges.full_bridge_optimizer`](@ref) which automatically select the
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appropriate bridges for unsupported constrained variables.
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#### Constraint reformulation
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A constraint often possess different equivalent formulations, but a solver may only support one of them.
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It would be duplicate work to implement rewritting rules in every solver wrapper for every different formulation of the constraint to express it in the form supported by the solver.
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Constraint bridges provide a way to define a rewritting rule on top of the MOI interface which can be used by any optimizer.
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Some rules also implement constraint modifications and constraint primal and duals translations.
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For example, the `SplitIntervalBridge` defines the reformulation of a `ScalarAffineFunction`-in-`Interval` constraint into a `ScalarAffineFunction`-in-`GreaterThan` and a `ScalarAffineFunction`-in-`LessThan` constraint.
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The `SplitInterval` is the bridge optimizer that applies the `SplitIntervalBridge` rewritting rule.
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Given an optimizer `optimizer` implementing `ScalarAffineFunction`-in-`GreaterThan` and `ScalarAffineFunction`-in-`LessThan`, the optimizer
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```
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bridgedoptimizer = SplitInterval(optimizer)
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For example, the [`Bridges.Constraint.SplitIntervalBridge`](@ref) defines the
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reformulation of a [`ScalarAffineFunction`](@ref)-in-[`Interval`](@ref)
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constraint into a [`ScalarAffineFunction`](@ref)-in-[`GreaterThan`](@ref) and a
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[`ScalarAffineFunction`](@ref)-in-[`LessThan`](@ref) constraint.
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The `Bridges.Constraint.SplitInterval` is the bridge optimizer that applies the
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[`Bridges.Constraint.SplitIntervalBridge`](@ref) rewritting rule. Given an
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optimizer `optimizer` implementing [`ScalarAffineFunction`](@ref)-in-[`GreaterThan`](@ref)
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and [`ScalarAffineFunction`](@ref)-in-[`LessThan`](@ref), the optimizer
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```jldoctest; setup=:(optimizer = MOI.Utilities.Model{Float64}())
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bridged_optimizer = MOI.Bridges.Constraint.SplitInterval{Float64}(optimizer)
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MOI.supports_constraint(bridged_optimizer, MOI.ScalarAffineFunction{Float64}, MOI.Interval{Float64})
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# output
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true
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```
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will additionally support `ScalarAffineFunction`-in-`Interval`.
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Note that these [`Bridges.Constraint.SingleBridgeOptimizer`](@ref) are mainly
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used for testing bridges. It is recommended to rather use
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[`Bridges.full_bridge_optimizer`](@ref) which automatically select the
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appropriate constraint bridges for unsupported constraints.
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## Implementing a solver interface
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‎docs/src/apireference.md‎

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submit
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```
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## Model Interface
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```@docs
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[`add_variables`](@ref) while *constrained variables* are
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the variables created with [`add_constrained_variable`](@ref) or
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[`add_constrained_variables`](@ref). Adding constrained variables instead of
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constraining free variables with [`add_constraint`](@ref) allows Variable
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bridges to be used.
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constraining free variables with [`add_constraint`](@ref) allows
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[Variable bridges](@ref) to be used.
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Note further that free variables that are constrained with
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[`add_constraint`](@ref) may be copied by [`copy_to`](@ref) with
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[`add_constrained_variable`](@ref) or [`add_constrained_variables`](@ref) by the
@@ -481,17 +480,219 @@ Utilities.@model
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## Bridges
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484-
Bridges can be used for automatic reformulation of a certain constraint type into equivalent constraints.
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Bridges can be used for automatic reformulation of constrained variables or
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constraints into equivalent formulations using constrained variables and
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constraints of different types. There are two important concepts to distinguish:
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* [`Bridges.AbstractBridge`](@ref)s are recipes implementing a specific
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reformulation. Bridges are not directly subtypes of
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[`Bridges.AbstractBridge`](@ref), they are either
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[`Bridges.Variable.AbstractBridge`](@ref) or
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[`Bridges.Constraint.AbstractBridge`](@ref).
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* [`Bridges.AbstractBridgeOptimizer`](@ref) is a layer that can be applied to
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another [`ModelLike`](@ref) to apply the reformulation. The
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[`Bridges.LazyBridgeOptimizer`](@ref) automatically chooses the appropriate
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bridges to use when a constrained variable or constraint is not supported
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by using the list of bridges that were added to it by
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[`Bridges.add_bridge`](@ref). [`Bridges.full_bridge_optimizer`](@ref) wraps a
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model in a [`Bridges.LazyBridgeOptimizer`](@ref) where all the bridges defined
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in MOI are added. This is the recommended way to use bridges in the
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[Testing guideline](@ref), and JuMP automatically calls this function when
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attaching an optimizer.
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485502
```@docs
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Bridges.AbstractBridge
487-
Bridges.Constraint.AbstractBridge
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Bridges.AbstractBridgeOptimizer
489-
Bridges.Constraint.SingleBridgeOptimizer
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Bridges.LazyBridgeOptimizer
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Bridges.add_bridge
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Bridges.full_bridge_optimizer
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```
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### Variable bridges
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When variables are added, either free with
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[`add_variable`](@ref)/[`add_variables`](@ref),
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or constrained with
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[`add_constrained_variable`](@ref)/[`add_constrained_variables`](@ref),
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variable bridges allow to return *bridged variables* that do not correspond to
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variables of the underlying model. These variables are parametrized by
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variables of the underlying model and this parametrization can be obtained with
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[`Bridges.bridged_variable_function`](@ref). Similarly, the variables of the
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underlying model that were created by the bridge can be expressed in terms of
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the bridged variables and this expression can be obtained with
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[`Bridges.unbridged_variable_function`](@ref).
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For instance, consider a model bridged by the
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[`Bridges.Variable.VectorizeBridge`](@ref):
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```jldoctest bridged_variable_function
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model = MOI.Utilities.Model{Float64}()
527+
bridged_model = MOI.Bridges.Variable.Vectorize{Float64}(model)
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bridged_variable, bridged_constraint = MOI.add_constrained_variable(bridged_model, MOI.GreaterThan(1.0))
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# output
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(MOI.VariableIndex(-1), MOI.ConstraintIndex{MOI.SingleVariable,MOI.GreaterThan{Float64}}(-1))
533+
```
534+
The constrained variable in `MOI.GreaterThan(1.0)` returned is a bridged
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variable as its index in negative. In `model`, a constrained variable in
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`MOI.Nonnegatives` is created:
537+
```jldoctest bridged_variable_function
538+
inner_variables = MOI.get(model, MOI.ListOfVariableIndices())
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# output
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1-element Array{MOI.VariableIndex,1}:
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MOI.VariableIndex(1)
544+
```
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In the functions used for adding constraints or setting the objective to
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`bridged_model`, `bridged_variable` is substituted for `inner_variables[1]` plus
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1:
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```jldoctest bridged_variable_function
549+
MOI.Bridges.bridged_variable_function(bridged_model, bridged_variable)
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# output
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MOI.ScalarAffineFunction{Float64}(MOI.ScalarAffineTerm{Float64}[ScalarAffineTerm{Float64}(1.0, VariableIndex(1))], 1.0)
554+
```
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When getting [`ConstraintFunction`](@ref) or [`ObjectiveFunction`](@ref),
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`inner_variables[1]` is substituted for `bridged_variable` minus 1:
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```jldoctest bridged_variable_function
558+
MOI.Bridges.unbridged_variable_function(bridged_model, inner_variables[1])
559+
560+
# output
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562+
MOI.ScalarAffineFunction{Float64}(MOI.ScalarAffineTerm{Float64}[ScalarAffineTerm{Float64}(1.0, VariableIndex(-1))], -1.0)
563+
```
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566+
!!! note
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A notable exception is with [`Bridges.Variable.ZerosBridge`](@ref) where no
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variable is created in the underlying model as the variables are simply
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transformed to zeros. When this bridge is used, it is not possible to
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recover functions with bridged variables from functions of the inner
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model. Consider for instance that we create two zero variables:
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```jldoctest cannot_unbridge_zero
573+
model = MOI.Utilities.Model{Float64}()
574+
bridged_model = MOI.Bridges.Variable.Zeros{Float64}(model)
575+
bridged_variables, bridged_constraint = MOI.add_constrained_variables(bridged_model, MOI.Zeros(2))
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# output
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579+
(MOI.VariableIndex[VariableIndex(-1), VariableIndex(-2)], MOI.ConstraintIndex{MOI.VectorOfVariables,MOI.Zeros}(-1))
580+
```
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Consider the following functions in the variables of `bridged_model`:
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```jldoctest cannot_unbridge_zero
583+
func = MOI.Utilities.operate(+, Float64, MOI.SingleVariable.(bridged_variables)...)
584+
585+
# output
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587+
MOI.ScalarAffineFunction{Float64}(MOI.ScalarAffineTerm{Float64}[ScalarAffineTerm{Float64}(1.0, VariableIndex(-1)), ScalarAffineTerm{Float64}(1.0, VariableIndex(-2))], 0.0)
588+
```
589+
We can obtain the equivalent function in the variables of `model` as follows:
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```jldoctest cannot_unbridge_zero
591+
inner_func = MOI.Bridges.bridged_function(bridged_model, func)
592+
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# output
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595+
MOI.ScalarAffineFunction{Float64}(MOI.ScalarAffineTerm{Float64}[], 0.0)
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```
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However, it's not possible to invert this operations. Indeed, since the
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bridged variables are substituted for zeros, we cannot deduce whether
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they were present in the initial function.
600+
```jldoctest cannot_unbridge_zero; filter = r"Stacktrace:.*"s
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MOI.Bridges.unbridged_function(bridged_model, inner_func)
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# output
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ERROR: Cannot unbridge function because some variables are bridged by variable bridges that do not support reverse mapping, e.g., `ZerosBridge`.
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Stacktrace:
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[1] error(::String, ::String, ::String) at ./error.jl:42
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[2] throw_if_cannot_unbridge at /home/blegat/.julia/dev/MathOptInterface/src/Bridges/Variable/map.jl:343 [inlined]
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[3] unbridged_function(::MOI.Bridges.Variable.SingleBridgeOptimizer{MOI.Bridges.Variable.ZerosBridge{Float64},MOI.Utilities.Model{Float64}}, ::MOI.ScalarAffineFunction{Float64}) at /home/blegat/.julia/dev/MOI/src/Bridges/bridge_optimizer.jl:920
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[4] top-level scope at none:0
611+
```
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613+
```@docs
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Bridges.Variable.AbstractBridge
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Bridges.bridged_variable_function
616+
Bridges.unbridged_variable_function
492617
```
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494-
Below is the list of bridges implemented in this package.
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Below is the list of variable bridges implemented in this package.
620+
```@docs
621+
Bridges.Variable.ZerosBridge
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Bridges.Variable.FreeBridge
623+
Bridges.Variable.NonposToNonnegBridge
624+
Bridges.Variable.VectorizeBridge
625+
Bridges.Variable.RSOCtoPSDBridge
626+
```
627+
628+
For each bridge defined in this package, a corresponding
629+
[`Bridges.Variable.SingleBridgeOptimizer`](@ref) is available with the same
630+
name without the "Bridge" suffix, e.g., `SplitInterval` is a
631+
`SingleBridgeOptimizer` for the `SplitIntervalBridge`. Moreover, they are all
632+
added in the [`Bridges.LazyBridgeOptimizer`](@ref) returned by
633+
[`Bridges.full_bridge_optimizer`](@ref) as it calls
634+
[`Bridges.Variable.add_all_bridges`](@ref).
635+
```@docs
636+
Bridges.Variable.SingleBridgeOptimizer
637+
Bridges.Variable.add_all_bridges
638+
```
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640+
### Constraint bridges
641+
642+
When constraints are added with [`add_constraint`](@ref), constraint bridges
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allow to return *bridged constraints* that do not correspond to
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constraints of the underlying model. These constraints were enforced by an
645+
equivalent formulation that added constraints (and possibly also variables) in
646+
the underlying model.
647+
For instance, consider a model bridged by the
648+
[`Bridges.Constraint.SplitIntervalBridge`](@ref):
649+
```jldoctest split_interval
650+
model = MOI.Utilities.Model{Float64}()
651+
bridged_model = MOI.Bridges.Constraint.SplitInterval{Float64}(model)
652+
x, y = MOI.add_variables(bridged_model, 2)
653+
func = MOI.Utilities.operate(+, Float64, MOI.SingleVariable(x), MOI.SingleVariable(y))
654+
c = MOI.add_constraint(bridged_model, func, MOI.Interval(1.0, 2.0))
655+
656+
# output
657+
658+
MOI.ConstraintIndex{MOI.ScalarAffineFunction{Float64},MOI.Interval{Float64}}(1)
659+
```
660+
We can see the constraint was bridged to two constraints, one for each bound,
661+
in the inner model.
662+
```jldoctest split_interval
663+
MOI.get(model, MOI.ListOfConstraints())
664+
665+
# output
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667+
2-element Array{Tuple{DataType,DataType},1}:
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(MOI.ScalarAffineFunction{Float64}, MOI.GreaterThan{Float64})
669+
(MOI.ScalarAffineFunction{Float64}, MOI.LessThan{Float64})
670+
```
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However, `bridged_model` hides transparently hides these constraints and create the
672+
illusion that an interval constraint was created.
673+
```jldoctest split_interval
674+
MOI.get(bridged_model, MOI.ListOfConstraints())
675+
676+
# output
677+
678+
1-element Array{Tuple{DataType,DataType},1}:
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(MOI.ScalarAffineFunction{Float64}, MOI.Interval{Float64})
680+
```
681+
It is nevertheless possible to differentiate this constraint from a constraint
682+
added to the inner model by asking whether it is bridged:
683+
```jldoctest split_interval
684+
MOI.Bridges.is_bridged(bridged_model, c)
685+
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# output
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688+
true
689+
```
690+
691+
```@docs
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Bridges.Constraint.AbstractBridge
693+
```
694+
695+
Below is the list of constraint bridges implemented in this package.
495696
```@docs
496697
Bridges.Constraint.GreaterToLessBridge
497698
Bridges.Constraint.LessToGreaterBridge
@@ -514,20 +715,36 @@ Bridges.Constraint.SOCtoPSDBridge
514715
Bridges.Constraint.RSOCtoPSDBridge
515716
Bridges.Constraint.IndicatorActiveOnFalseBridge
516717
```
517-
For each bridge defined in this package, a corresponding bridge optimizer is available with the same name without the "Bridge" suffix, e.g., `SplitInterval` is an `SingleBridgeOptimizer` for the `SplitIntervalBridge`.
518-
Moreover, a `LazyBridgeOptimizer` with all the bridges defined in this package can be obtained with
718+
For each bridge defined in this package, a corresponding
719+
[`Bridges.Constraint.SingleBridgeOptimizer`](@ref) is available with the same
720+
name without the "Bridge" suffix, e.g., `SplitInterval` is a
721+
`SingleBridgeOptimizer` for the `SplitIntervalBridge`. Moreover, they are all
722+
added in the [`Bridges.LazyBridgeOptimizer`](@ref) returned by
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[`Bridges.full_bridge_optimizer`](@ref) as it calls
724+
[`Bridges.Constraint.add_all_bridges`](@ref).
519725
```@docs
520-
Bridges.full_bridge_optimizer
726+
Bridges.Constraint.SingleBridgeOptimizer
727+
Bridges.Constraint.add_all_bridges
521728
```
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523730
### Bridge interface
524731

525732
A bridge should implement the following functions to be usable by a bridge optimizer:
526733
```@docs
734+
Bridges.added_constrained_variable_types
735+
Bridges.added_constraint_types
736+
```
737+
Additionally, variable bridges should implement:
738+
```@docs
739+
Bridges.Variable.supports_constrained_variable
740+
Bridges.Variable.concrete_bridge_type
741+
Bridges.Variable.bridge_constrained_variable
742+
```
743+
and constraint bridges should implement
744+
```@docs
527745
supports_constraint(::Type{<:Bridges.Constraint.AbstractBridge}, ::Type{<:AbstractFunction}, ::Type{<:AbstractSet})
528746
Bridges.Constraint.concrete_bridge_type
529747
Bridges.Constraint.bridge_constraint
530-
Bridges.added_constraint_types
531748
```
532749

533750
When querying the [`NumberOfVariables`](@ref), [`NumberOfConstraints`](@ref)
@@ -538,8 +755,9 @@ constraints it has creates by implemented the following methods of
538755
[`get`](@ref):
539756
```@docs
540757
get(::Bridges.Constraint.AbstractBridge, ::NumberOfVariables)
541-
get(::Bridges.Constraint.AbstractBridge, ::NumberOfConstraints)
542-
get(::Bridges.Constraint.AbstractBridge, ::ListOfConstraintIndices)
758+
get(::Bridges.Constraint.AbstractBridge, ::ListOfVariableIndices)
759+
get(::Bridges.AbstractBridge, ::NumberOfConstraints)
760+
get(::Bridges.AbstractBridge, ::ListOfConstraintIndices)
543761
```
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545763
## Copy utilities
@@ -645,7 +863,7 @@ is set to `AUTOMATIC` or to `MANUAL`.
645863
a constraint) results in a drop to the state `EMPTY_OPTIMIZER`.
646864

647865
When calling [`Utilities.attach_optimizer`](@ref), the `CachingOptimizer` copies
648-
the cached model to the optimizer with [`MathOptInterface.copy_to`](@ref).
866+
the cached model to the optimizer with [`copy_to`](@ref).
649867
We refer to [Implementing copy](@ref) for more details.
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```@docs

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