From 454f0cb69768e057bf7d06c7b19e1c7161320ca3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Mathieu=20Besan=C3=A7on?= <mathieu.besancon@gmail.com>
Date: Sun, 4 Jul 2021 17:45:59 +0200
Subject: [PATCH] valid inequalities first draft

---
 src/jump_attributes.jl    |  2 +-
 src/valid_inequalities.jl | 67 +++++++++++++++++++++++++++++++++++++++
 2 files changed, 68 insertions(+), 1 deletion(-)
 create mode 100644 src/valid_inequalities.jl

diff --git a/src/jump_attributes.jl b/src/jump_attributes.jl
index 71e36930..ac840d0e 100644
--- a/src/jump_attributes.jl
+++ b/src/jump_attributes.jl
@@ -95,4 +95,4 @@ function unset_pass_start(bm::BilevelModel)
 end
 function get_pass_start(bm::BilevelModel)
     return bm.pass_start
-end
\ No newline at end of file
+end
diff --git a/src/valid_inequalities.jl b/src/valid_inequalities.jl
new file mode 100644
index 00000000..0e7321c3
--- /dev/null
+++ b/src/valid_inequalities.jl
@@ -0,0 +1,67 @@
+
+"""
+Build the subproblem for valid inequalities
+```
+min_{x,v,λ} 0
+            G x + H v ≤ q (upper level constraints)
+            A x + B v ≤ b (lower level constraints)
+            d + B^T λ ≥ 0 (dual lower level constraints)
+            x ∈ X (upper level other constraints)
+```
+The objective `A_i ⋅ x` can then be set later.
+"""
+function build_inequality_subproblem_constraints(bilevel_model::AbstractBilevelModel; optimizer=nothing)
+
+    m = Model()
+    if optimizer !== nothing
+        set_optimizer(model, optimizer)
+    end
+    # Add variables from both levels
+
+    # Copy UL and LL constraints
+
+    # Dualize lower-level model and add constraints
+
+    return m
+end
+
+"""
+Takes a bilevel model and the `submodel` built by `build_inequality_subproblem_constraints`,
+sets the objective as `max_x func(cons)`, the function of the passed linear constraint of the form affine-function less than constant.
+If the constraint is of the form: `a ⋅ x + b ⋅ y ≤ c`, this corresponds to `max_x a ⋅ x`.
+The constraint must be a lower level one.
+"""
+function set_optimize_inequality_subproblem(bilevel_model::AbstractBilevelModel, submodel::JuMP.AbstractModel, cons::ConstraintRef{<:BilevelJuMP.AbstractBilevelModel})
+    # TODO get vector of upper-level constraints
+    x = nothing
+    cobj = constraint_object(cons)
+    objective_func = AffExpr()
+    sign_multiplier = if cobj.set isa MOI.GreaterThan
+        1
+    elseif cobj.set isa MOI.GreaterThan
+        sign_multiplier = -1
+    else
+        # equality not handled because value would be trivial / independent of x
+        error("Constraint should be an inequality")
+    end
+    for (var, coeff) in cres.func.terms
+        xi = nothing # TODO find variable corresponding to var in submodel
+        add_to_expression!(objective_func, xi, sign_multiplier * coeff)
+    end
+    set_objective_function(submodel, objective_func)
+    set_objective_sense(submodel, MOI.MIN_SENSE)
+    return submodel
+end
+
+function compute_valid_inequalities(bilevel_model::AbstractBilevelModel; max_iterations=50, optimizer=nothing)
+    submodel = build_inequality_subproblem_constraints(bilevel_model, optimizer=optimizer)
+    # tuples with the constraint and the current count
+    constraint_count = []
+    for (F, S) in list_of_constraint_types(Lower(bilevel_model))
+        if F <: GenericAffExpr
+            for cons in all_constraints(Lower(bilevel_model), F, S)
+                push!(constraint_count, (cons, 0))
+            end
+        end
+    end
+end