A bilevel linear optimization problem of the form:

min cx^T * x + cy^T * y
s.t. G x + H y <= q
     x_j ∈ [xl_j,xu_j]
     x_j ∈ ℤ ∀ j ∈ Jx
     y ∈ arg min {
        d^T * y + x^T * F * y
        s.t. A x + B y <= b
             y_j ∈ [yl_j,yu_j]
        }

Note that integer variables are allowed at the upper level.

BoundComplementarity{MD,MP}

Represent complementarity constraints implemented using big-M bounds on primal and dual variables.

Handle complementarity constraints with Special Ordered Sets of type 1

VariableType enum distinguishing upper- and lower-level variables for setting upper and lower bounds

`build_blp_model(bp::BilevelLP, solver; [comp_method])`

Build a JuMP model (constraints and objective) based on the data from bp and with a solver.

Returns a tuple (m, x, y, λ, s).

An optional keyword comp_method can be passed for handling complementarity constraints, default is SOS1Complementarity.

`build_blp_model(m::JuMP.Model, bp::BilevelLP, x, y; [comp_method])`

Adds the lower-level constraints and optimality conditions to an existing JuMP model. This assumes the upper-level feasibility constraints and objective have already been set.

Returns a tuple (m, x, y, λ, s).

An optional keyword comp_method can be passed for handling complementarity constraints, default is SOS1Complementarity.

`build_blp_model(m, B, d, x, y, s, F; [comp_method])`

Build the bilevel JuMP model from the data without grouping everything into a BilevelLP. An optional keyword comp_method can be passed for handling complementarity constraints, default is SOS1Complementarity.

Method used for handling complementarity constraints s[i] ⋅ λ[i] = 0 Must implement:

add_complementarity_constraint(m, cm::ComplementarityMethod, s, λ)

Convenience alias for a matrix of a sub-type of Real

Convenience alias for a vector of a sub-type of Real

Add dual bounds with one bound for each element

Add dual bounds with one same bound for all elements

Add primal bounds with one bound for each element

Add primal bounds with the same bound for all elements

Add complementarity constraints to the JuMP model m for each pair (s[i],λ[i]) with the corresponding complementarity method.

add_complementarity_constraint(m, cm::ComplementarityMethod, s, λ, y, σ)

add_complementarity_constraint(m, bc::BoundComplementarity, s, λ, y, σ)

Implement complementarity constraints using big-M type constraints. This formulation introduces binary variables:

active_constraint[i] == 0 <=> λ[i] == 0
active_constraint[i] == 1 <=> s[i] == 0
variable_bound[j] == 0 <=> σ[j] == 0
variable_bound[j] == 1 <=> y[j] == 0

add_complementarity_constraint(m, ::SOS1Complementarity, s, λ, y, σ)

Implements complementarity constraints using special ordered sets 1 (SOS1).

Set a lower bound on a lower or higher variable of bp depending on vartype

Set an upper bound on a lower or higher variable of bp depending on vartype Since we need the dual for lower-level upper bounds, this case is registered as a constraint.