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Sep 4, 2021
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[Bridges] maintenance of relentr_to_exp.jl #1579

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88 changes: 51 additions & 37 deletions src/Bridges/Constraint/relentr_to_exp.jl
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Original file line number Diff line number Diff line change
@@ -1,16 +1,17 @@
"""
RelativeEntropyBridge{T}

The `RelativeEntropyCone` is representable with exponential cone and LP constraints, since
``u \\ge \\sum_{i=1}^n w_i \\log (\\frac{w_i}{v_i})`` if and only if there exists a vector
``y`` such that ``u \\ge \\sum_i y_i`` and ``y_i \\ge w_i \\log (\\frac{w_i}{v_i})`` or
equivalently ``v_i \\ge w_i \\exp (\\frac{-y_i}{w_i})`` or equivalently
The `RelativeEntropyCone` is representable with exponential cone and LP
constraints, since ``u \\ge \\sum_{i=1}^n w_i \\log (\\frac{w_i}{v_i})`` if and
only if there exists a vector ``y`` such that ``u \\ge \\sum_i y_i`` and
``y_i \\ge w_i \\log (\\frac{w_i}{v_i})`` or equivalently
``v_i \\ge w_i \\exp (\\frac{-y_i}{w_i})`` or equivalently
``(-y_i, w_i, v_i) \\in ExponentialCone``, for all ``i``.
"""
struct RelativeEntropyBridge{T,F,G,H} <: AbstractBridge
y::Vector{MOI.VariableIndex}
ge_index::CI{F,MOI.GreaterThan{T}}
exp_indices::Vector{CI{G,MOI.ExponentialCone}}
ge_index::MOI.ConstraintIndex{F,MOI.GreaterThan{T}}
exp_indices::Vector{MOI.ConstraintIndex{G,MOI.ExponentialCone}}
end

function bridge_constraint(
Expand All @@ -19,23 +20,23 @@ function bridge_constraint(
f::H,
s::MOI.RelativeEntropyCone,
) where {T,F,G,H}
f_scalars = MOIU.eachscalar(f)
f_scalars = MOI.Utilities.eachscalar(f)
d = MOI.dimension(s)
v_dim = div(d - 1, 2)
y = MOI.add_variables(model, v_dim)
rhs = MOI.ScalarAffineFunction(MOI.ScalarAffineTerm.(one(T), y), zero(T))
ge_index = MOIU.normalize_and_add_constraint(
ge_index = MOI.Utilities.normalize_and_add_constraint(
model,
MOIU.operate(-, T, f_scalars[1], rhs),
MOI.Utilities.operate(-, T, f_scalars[1], rhs),
MOI.GreaterThan(zero(T)),
allow_modify_function = true,
)
w_start = 1 + v_dim
exp_funcs = [
MOIU.operate(
MOI.Utilities.operate(
vcat,
T,
MOIU.operate(-, T, y[i]),
MOI.Utilities.operate(-, T, y[i]),
f_scalars[w_start+i],
f_scalars[1+i],
) for i in 1:v_dim
Expand All @@ -55,11 +56,13 @@ function MOI.supports_constraint(
return true
end

function MOIB.added_constrained_variable_types(::Type{<:RelativeEntropyBridge})
function MOI.Bridges.added_constrained_variable_types(
::Type{<:RelativeEntropyBridge},
)
return Tuple{Type}[]
end

function MOIB.added_constraint_types(
function MOI.Bridges.added_constraint_types(
::Type{RelativeEntropyBridge{T,F,G,H}},
) where {T,F,G,H}
return Tuple{Type,Type}[(F, MOI.GreaterThan{T}), (G, MOI.ExponentialCone)]
Expand All @@ -70,18 +73,17 @@ function concrete_bridge_type(
H::Type{<:MOI.AbstractVectorFunction},
::Type{MOI.RelativeEntropyCone},
) where {T}
S = MOIU.scalar_type(H)
F = MOIU.promote_operation(-, T, S, S)
G = MOIU.promote_operation(
S = MOI.Utilities.scalar_type(H)
F = MOI.Utilities.promote_operation(-, T, S, S)
G = MOI.Utilities.promote_operation(
vcat,
T,
MOIU.promote_operation(-, T, MOI.VariableIndex),
MOI.Utilities.promote_operation(-, T, MOI.VariableIndex),
S,
)
return RelativeEntropyBridge{T,F,G,H}
end

# Attributes, Bridge acting as a model
function MOI.get(bridge::RelativeEntropyBridge, ::MOI.NumberOfVariables)::Int64
return length(bridge.y)
end
Expand Down Expand Up @@ -118,7 +120,6 @@ function MOI.get(
return copy(bridge.exp_indices)
end

# References
function MOI.delete(model::MOI.ModelLike, bridge::RelativeEntropyBridge)
for exp_index_i in bridge.exp_indices
MOI.delete(model, exp_index_i)
Expand All @@ -128,14 +129,13 @@ function MOI.delete(model::MOI.ModelLike, bridge::RelativeEntropyBridge)
return
end

# Attributes, Bridge acting as a constraint
function MOI.get(
model::MOI.ModelLike,
::MOI.ConstraintFunction,
bridge::RelativeEntropyBridge{T,F,G,H},
) where {T,F,G,H}
func = MOIU.zero_with_output_dimension(G, 1 + 2 * length(bridge.y))
MOIU.operate_output_index!(
func = MOI.Utilities.zero_with_output_dimension(G, 1 + 2 * length(bridge.y))
MOI.Utilities.operate_output_index!(
+,
T,
1,
Expand All @@ -144,30 +144,41 @@ function MOI.get(
)
w_start = 1 + length(bridge.y)
for i in eachindex(bridge.y)
exp_func_i = MOIU.eachscalar(
exp_func_i = MOI.Utilities.eachscalar(
MOI.get(model, MOI.ConstraintFunction(), bridge.exp_indices[i]),
)
MOIU.operate_output_index!(-, T, 1, func, exp_func_i[1])
MOIU.operate_output_index!(+, T, 1 + i, func, exp_func_i[3])
MOIU.operate_output_index!(+, T, w_start + i, func, exp_func_i[2])
MOI.Utilities.operate_output_index!(-, T, 1, func, exp_func_i[1])
MOI.Utilities.operate_output_index!(+, T, 1 + i, func, exp_func_i[3])
MOI.Utilities.operate_output_index!(
+,
T,
w_start + i,
func,
exp_func_i[2],
)
end
return MOIU.convert_approx(H, MOIU.remove_variable(func, bridge.y))
return MOI.Utilities.convert_approx(
H,
MOI.Utilities.remove_variable(func, bridge.y),
)
end

function MOI.get(
model::MOI.ModelLike,
::MOI.ModelLike,
::MOI.ConstraintSet,
bridge::RelativeEntropyBridge,
)
return MOI.RelativeEntropyCone(1 + 2 * length(bridge.y))
end

function MOI.supports(
::MOI.ModelLike,
::Union{MOI.ConstraintPrimalStart,MOI.ConstraintDualStart},
::Type{<:RelativeEntropyBridge},
)
return true
model::MOI.ModelLike,
attr::Union{MOI.ConstraintPrimalStart,MOI.ConstraintDualStart},
::Type{RelativeEntropyBridge{T,F,G,H}},
) where {T,F,G,H}
ci_1 = MOI.ConstraintIndex{F,MOI.GreaterThan{T}}
ci_2 = MOI.ConstraintIndex{G,MOI.ExponentialCone}
return MOI.supports(model, attr, ci_1) && MOI.supports(model, attr, ci_2)
end

function MOI.get(
Expand Down Expand Up @@ -214,8 +225,10 @@ function MOI.set(
end
return
end
# Given a is dual on u - sum(y) >= 0 and (b_i, c_i, d_i) is dual on (-y_i, w_i, v_i)
# in ExponentialCone, the dual on (u, v, w) in RelativeEntropyCone is (a, d_i, c_i).

# Given a is dual on u - sum(y) >= 0 and (b_i, c_i, d_i) is dual on
# (-y_i, w_i, v_i) in ExponentialCone, the dual on
# (u, v, w) in RelativeEntropyCone is (a, d_i, c_i).
function MOI.get(
model::MOI.ModelLike,
attr::Union{MOI.ConstraintDual,MOI.ConstraintDualStart},
Expand All @@ -231,9 +244,10 @@ function MOI.get(
end
return dual
end

# Given constraint dual start of (u, v, w), constraint dual on GreaterThan is u
# and on exponential cone constraint i is (r_i, w_i, v_i), but since y_i is free,
# its dual is 0, so we have -r_i + u == 0 hence r_i = u.
# and on exponential cone constraint i is (r_i, w_i, v_i), but since y_i is
# free, its dual is 0, so we have -r_i + u == 0 hence r_i = u.
# Note: alternatively, we could use the Lambert W function to calculate
# r_i = exp(W(-w_i / (-v_i * e))) * (-v_i * e), but this is more complicated.
function MOI.set(
Expand Down