diff --git a/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl b/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl index baae693cbc..7dd5d9f0b0 100644 --- a/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl +++ b/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl @@ -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