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[Utilities] add distance_to_set for more sets #2925

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Merged
odow merged 1 commit into from
Jan 29, 2026
Merged

[Utilities] add distance_to_set for more sets #2925

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138 changes: 116 additions & 22 deletions src/Utilities/distance_to_set.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -175,6 +175,39 @@ function _check_dimension(v::AbstractVector, s)
return
end

function _reshape(
x::AbstractVector,
set::Union{
MOI.PositiveSemidefiniteConeSquare,
MOI.LogDetConeSquare,
MOI.RootDetConeSquare,
},
)
n = isqrt(length(x))
return reshape(x, (n, n))
end

function _reshape(
x::AbstractVector{T},
set::Union{
MOI.PositiveSemidefiniteConeTriangle,
MOI.LogDetConeTriangle,
MOI.RootDetConeTriangle,
},
) where {T}
n = isqrt(2 * length(x))
# The type annotation is needed for JET.
X = zeros(T, n, n)::Matrix{T}
k = 1
for i in 1:n
for j in 1:i
X[j, i] = X[i, j] = x[k]
k += 1
end
end
return LinearAlgebra.Symmetric(X)
end

# This is the minimal L2-norm.
function distance_to_set(
::ProjectionUpperBoundDistance,
Expand Down Expand Up @@ -499,28 +532,6 @@ function distance_to_set(
return LinearAlgebra.norm(elements, 2)
end

function _reshape(x::AbstractVector, set::MOI.PositiveSemidefiniteConeSquare)
n = MOI.side_dimension(set)
return reshape(x, (n, n))
end

function _reshape(
x::AbstractVector{T},
set::MOI.PositiveSemidefiniteConeTriangle,
) where {T}
n = MOI.side_dimension(set)
# The type annotation is needed for JET.
X = zeros(T, n, n)::Matrix{T}
k = 1
for i in 1:n
for j in 1:i
X[j, i] = X[i, j] = x[k]
k += 1
end
end
return LinearAlgebra.Symmetric(X)
end

"""
distance_to_set(
::ProjectionUpperBoundDistance,
Expand Down Expand Up @@ -608,3 +619,86 @@ function distance_to_set(
sqrt(x[1]^2 + distance_to_set(distance, x[2], set.set)^2),
)
end

"""
distance_to_set(::ProjectionUpperBoundDistance, x, set::MOI.NormNuclearCone)

Let `(t, y...) = x`. Return the epigraph distance `d` such that `(t + d, y...)`
belongs to the set.
"""
function distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector{T},
set::MOI.NormNuclearCone,
) where {T}
_check_dimension(x, set)
X = reshape(x[2:end], set.row_dim, set.column_dim)
return max(sum(LinearAlgebra.svdvals(X)) - x[1], zero(T))
end

"""
distance_to_set(::ProjectionUpperBoundDistance, x, set::MOI.NormSpectralCone)

Let `(t, y...) = x`. Return the epigraph distance `d` such that `(t + d, y...)`
belongs to the set.
"""
function distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector{T},
set::MOI.NormSpectralCone,
) where {T}
_check_dimension(x, set)
X = reshape(x[2:end], set.row_dim, set.column_dim)
return max(maximum(LinearAlgebra.svdvals(X)) - x[1], zero(T))
end

"""
distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector,
set::Union{MOI.RootDetConeSquare,MOI.RootDetConeTriangle},
)

Let ``Y`` be `y` in `x = (t, y)`, reshaped into the appropriate matrix. The
returned distance is ``||Y - Z||_2^2`` where ``Z`` is the eigen decomposition of
``Y`` with negative eigen values removed, plus the epigraph distance in `t`
needed to satisfy the root-determinant constraint.
"""
function distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector{T},
set::Union{MOI.RootDetConeSquare,MOI.RootDetConeTriangle},
) where {T<:Real}
_check_dimension(x, set)
eigvals = LinearAlgebra.eigvals(_reshape(x[2:end], set))
eigvals_neg = min.(zero(T), eigvals)
eigvals_pos = max.(zero(T), eigvals)
rootdet = prod(eigvals_pos)^(1 / set.side_dimension)
push!(eigvals_neg, max(x[1] - rootdet, zero(T)))
return LinearAlgebra.norm(eigvals_neg, 2)
end

"""
distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector,
set::Union{MOI.LogDetConeSquare,MOI.LogDetConeTriangle},
)

Let ``Y`` be `y` in `x = (t, y)`, reshaped into the appropriate matrix. The
returned distance is ``||Y/u - Z||_2^2`` where ``Z`` is the eigen decomposition
of ``Y`` with negative eigen values removed, plus the epigraph distance in `t`
needed to satisfy the log-determinant constraint.
"""
function distance_to_set(
::ProjectionUpperBoundDistance,
x::AbstractVector{T},
set::Union{MOI.LogDetConeSquare,MOI.LogDetConeTriangle},
) where {T<:Real}
_check_dimension(x, set)
eigvals = LinearAlgebra.eigvals(_reshape(x[3:end] ./ x[2], set))
eigvals_neg = min.(eps(T), eigvals)
eigvals_pos = max.(eps(T), eigvals)
push!(eigvals_neg, max(x[1] - x[2] * sum(log.(eigvals_pos)), zero(T)))
return LinearAlgebra.norm(eigvals_neg, 2)
end
78 changes: 77 additions & 1 deletion test/Utilities/distance_to_set.jl
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -394,7 +394,83 @@ function test_indicator()
[0.99, 1.0] => 0.01,
[0.99, 1.1] => sqrt(0.01^2 + 0.1^2),
[0.5, 1.1] => 0.5,
[0.8, 1.1] => sqrt(0.2^2 + 0.1^2),
[0.8, 1.1] => sqrt(0.2^2 + 0.1^2);
mismatch = [1.0],
)
return
end

function test_NormNuclearCone()
_test_set(
MOI.NormNuclearCone(2, 3),
[0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] => 10.039818672223756,
[11.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] => 0.0;
mismatch = [1.0],
)
return
end

function test_NormSpectralCone()
_test_set(
MOI.NormSpectralCone(2, 3),
[0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] => 9.525518091565111,
[9.6, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0] => 0.0;
mismatch = [1.0],
)
return
end

function test_RootDetConeTriangle()
_test_set(
MOI.RootDetConeTriangle(2),
[2.0, 1.0, 0.0, 1.0] => 1.0,
[0.9, 1.0, 0.0, 1.0] => 0.0,
[2.0, 1.0, 0.0, 2.0] => 2 - sqrt(2),
# Projection onto PSD
[0.0, 1.0, 2.0, 3.0] => 0.2360679774997897,
# Projection onto PSD+t
[1.0, 1.0, 2.0, 3.0] => sqrt(1 + 0.2360679774997897^2);
mismatch = [1.0],
)
return
end

function test_RootDetConeSquare()
_test_set(
MOI.RootDetConeSquare(2),
[2.0, 1.0, 0.0, 0.0, 1.0] => 1.0,
[0.9, 1.0, 0.0, 0.0, 1.0] => 0.0,
[2.0, 1.0, 0.0, 0.0, 2.0] => 2 - sqrt(2),
# Projection onto PSD
[0.0, 1.0, 2.0, 2.0, 3.0] => 0.2360679774997897,
# Projection onto PSD+t
[1.0, 1.0, 2.0, 2.0, 3.0] => sqrt(1 + 0.2360679774997897^2);
mismatch = [1.0],
)
return
end

function test_LogDetConeTriangle()
_test_set(
MOI.LogDetConeTriangle(2),
[2.0, 1.0, 2.0, 0.0, 1.0] => 2 - 0.6931471805599453,
[0.69, 1.0, 2.0, 0.0, 1.0] => 0.0,
[0.0, 2.0, 2.0, 0.0, 1.0] => 1.3862943611198906,
mismatch = [1.0],
)
return
end

function test_LogDetConeSquare()
_test_set(
MOI.LogDetConeSquare(2),
[2.0, 1.0, 2.0, 0.0, 0.0, 1.0] => 2 - 0.6931471805599453,
[0.69, 1.0, 2.0, 0.0, 0.0, 1.0] => 0.0,
[0.0, 2.0, 2.0, 0.0, 0.0, 1.0] => 1.3862943611198906,
# Projection onto PSD
[0.0, 1.0, 1.0, 2.0, 2.0, 3.0] => 34.60082322336934,
# Projection onto PSD+t
[1.0, 1.0, 1.0, 2.0, 2.0, 3.0] => 35.60080060283381;
mismatch = [1.0],
)
return
Expand Down
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