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Merged
jd-lara merged 1 commit into from
Mar 5, 2026
Merged

update for formatter #34

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48 changes: 24 additions & 24 deletions docs/src/reference/quadratic_approximations.md
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Original file line number Diff line number Diff line change
Expand Up @@ -54,11 +54,11 @@ decreases as ``O(1/S^2)``.

### Variables and Constraints

| Container Type | Description |
|:---|:---|
| [`QuadraticApproxVariable`](@ref) | Lambda (``\lambda``) convex combination weights |
| [`QuadraticApproxLinkingConstraint`](@ref) | Links ``x`` to weighted breakpoints |
| [`QuadraticApproxNormalizationConstraint`](@ref) | Ensures ``\sum \lambda_i = 1`` |
| Container Type | Description |
|:------------------------------------------------ |:----------------------------------------------- |
| [`QuadraticApproxVariable`](@ref) | Lambda (``\lambda``) convex combination weights |
| [`QuadraticApproxLinkingConstraint`](@ref) | Links ``x`` to weighted breakpoints |
| [`QuadraticApproxNormalizationConstraint`](@ref) | Ensures ``\sum \lambda_i = 1`` |

## Manual SOS2

Expand Down Expand Up @@ -88,13 +88,13 @@ linear constraints per component per time step. Same approximation quality as So

### Variables and Constraints

| Container Type | Description |
|:---|:---|
| [`QuadraticApproxVariable`](@ref) | Lambda (``\lambda``) convex combination weights |
| [`ManualSOS2BinaryVariable`](@ref) | Binary segment-selection variables (``z``) |
| [`QuadraticApproxLinkingConstraint`](@ref) | Links ``x`` to weighted breakpoints |
| [`QuadraticApproxNormalizationConstraint`](@ref) | Ensures ``\sum \lambda_i = 1`` |
| [`ManualSOS2SegmentSelectionConstraint`](@ref) | Ensures ``\sum z_j = 1`` |
| Container Type | Description |
|:------------------------------------------------ |:----------------------------------------------- |
| [`QuadraticApproxVariable`](@ref) | Lambda (``\lambda``) convex combination weights |
| [`ManualSOS2BinaryVariable`](@ref) | Binary segment-selection variables (``z``) |
| [`QuadraticApproxLinkingConstraint`](@ref) | Links ``x`` to weighted breakpoints |
| [`QuadraticApproxNormalizationConstraint`](@ref) | Ensures ``\sum \lambda_i = 1`` |
| [`ManualSOS2SegmentSelectionConstraint`](@ref) | Ensures ``\sum z_j = 1`` |

## Sawtooth

Expand Down Expand Up @@ -143,21 +143,21 @@ constraints per component per time step. The approximation interpolates ``x^2``

### Variables and Constraints

| Container Type | Description |
|:---|:---|
| [`SawtoothAuxVariable`](@ref) | Auxiliary continuous variables (``g_0, \ldots, g_L``) |
| [`SawtoothBinaryVariable`](@ref) | Binary variables (``\alpha_1, \ldots, \alpha_L``) |
| [`SawtoothLinkingConstraint`](@ref) | Links ``g_0`` to normalized ``x`` |
| Container Type | Description |
|:----------------------------------- |:----------------------------------------------------- |
| [`SawtoothAuxVariable`](@ref) | Auxiliary continuous variables (``g_0, \ldots, g_L``) |
| [`SawtoothBinaryVariable`](@ref) | Binary variables (``\alpha_1, \ldots, \alpha_L``) |
| [`SawtoothLinkingConstraint`](@ref) | Links ``g_0`` to normalized ``x`` |

## Comparison

| Property | Solver SOS2 | Manual SOS2 | Sawtooth |
|:---|:---|:---|:---|
| Binary variables | 0 | ``S`` | ``L`` |
| Continuous variables | ``S + 1`` | ``S + 1`` | ``L + 1`` |
| Breakpoints | ``S + 1`` | ``S + 1`` | ``2^L + 1`` |
| Max error | ``O(\Delta^2 / S^2)`` | ``O(\Delta^2 / S^2)`` | ``\Delta^2 \cdot 2^{-2L-2}`` |
| Solver requirements | SOS2 support | MIP only | MIP only |
| Property | Solver SOS2 | Manual SOS2 | Sawtooth |
|:-------------------- |:--------------------- |:--------------------- |:---------------------------- |
| Binary variables | 0 | ``S`` | ``L`` |
| Continuous variables | ``S + 1`` | ``S + 1`` | ``L + 1`` |
| Breakpoints | ``S + 1`` | ``S + 1`` | ``2^L + 1`` |
| Max error | ``O(\Delta^2 / S^2)`` | ``O(\Delta^2 / S^2)`` | ``\Delta^2 \cdot 2^{-2L-2}`` |
| Solver requirements | SOS2 support | MIP only | MIP only |

To match the number of breakpoints between methods, set ``S = 2^L``. At equal breakpoint
count the approximation quality is identical, but the sawtooth uses ``L = \log_2 S``
Expand Down
10 changes: 5 additions & 5 deletions test/test_quadratic_approximations.jl
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Expand Up @@ -187,7 +187,7 @@ end

@testset "Approximation quality improves with more segments" begin
# min (√2)x² - (√3)x on [0, 6], analytic minimum at x=√3/8
analytic_min = sqrt(2)*(sqrt(3/8)^2) - sqrt(3)*sqrt(3/8)
analytic_min = sqrt(2) * (sqrt(3 / 8)^2) - sqrt(3) * sqrt(3 / 8)
errors = Float64[]
for num_segments in 2 .^ (1:6)
setup = _setup_qa_test(["dev1"], 1:1)
Expand All @@ -208,7 +208,7 @@ end
)
x_sq = result[("dev1", 1)]

JuMP.@objective(setup.jump_model, Min, sqrt(2)*x_sq - sqrt(3)*x_var)
JuMP.@objective(setup.jump_model, Min, sqrt(2) * x_sq - sqrt(3) * x_var)
JuMP.set_optimizer(setup.jump_model, HiGHS.Optimizer)
JuMP.set_silent(setup.jump_model)
JuMP.optimize!(setup.jump_model)
Expand Down Expand Up @@ -509,7 +509,7 @@ end

@testset "Approximation quality improves with depth" begin
# min (√2)x² - (√3)x on [0, 6], analytic minimum at x=√3/8
analytic_min = sqrt(2)*(sqrt(3/8)^2) - sqrt(3)*sqrt(3/8)
analytic_min = sqrt(2) * (sqrt(3 / 8)^2) - sqrt(3) * sqrt(3 / 8)
errors = Float64[]
for depth in 1:6
setup = _setup_qa_test(["dev1"], 1:1)
Expand All @@ -530,7 +530,7 @@ end
)
x_sq = result[("dev1", 1)]

JuMP.@objective(setup.jump_model, Min, sqrt(2)*x_sq - sqrt(3)*x_var)
JuMP.@objective(setup.jump_model, Min, sqrt(2) * x_sq - sqrt(3) * x_var)
JuMP.set_optimizer(setup.jump_model, HiGHS.Optimizer)
JuMP.set_silent(setup.jump_model)
JuMP.optimize!(setup.jump_model)
Expand Down Expand Up @@ -581,7 +581,7 @@ end
x_sq = result[("dev1", 1)]
end

JuMP.@objective(setup.jump_model, Min, sqrt(2)*x_sq - sqrt(3)*x_var)
JuMP.@objective(setup.jump_model, Min, sqrt(2) * x_sq - sqrt(3) * x_var)
JuMP.set_optimizer(setup.jump_model, HiGHS.Optimizer)
JuMP.set_silent(setup.jump_model)
JuMP.optimize!(setup.jump_model)
Expand Down
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