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Explain reformulation for SOS1ToMILP #2906

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odow merged 2 commits into from
Jan 13, 2026
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Explain reformulation for SOS1ToMILP #2906

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Explain reformulation for SOS1ToMILP
blegat Jan 13, 2026
644aaa7
Correct mathematical notation in SOS1ToMILPBridge
odow Jan 13, 2026
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11 changes: 10 additions & 1 deletion src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl
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Expand Up @@ -9,7 +9,16 @@

`SOS1ToMILPBridge` implements the following reformulation:

* ``x \\in \\textsf{SOS1}(d)`` into a mixed-integer linear program.
* ``x \\in \\textsf{SOS1}(d)`` into the following mixed-integer linear program.

Assuming ``l_i \\le x_i \\le u_i`` with finite bounds ``l_i``, ``u_i``:
```math
\\begin{aligned}
z_i \\in \\{0, 1\\} & \\;\\; \\forall i \\in 1\\ldots d \\\\
l_i z_i \\le x_i \\le u_i z_i & \\;\\; \\forall i \\in 1\\ldots d \\\\
\\sum z_i = 1
\\end{aligned}
```

## Source node

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