[docs] move manual section on Semicontinuous and Semiinteger variables (

#3562)

docs/src/manual/constraints.md

@@ -1296,34 +1296,6 @@ julia> @constraint(model, [t; u; x] in RotatedSecondOrderCone())
 [t, u, x[1], x[2]] ∈ MathOptInterface.RotatedSecondOrderCone(4)
 ```
 
-## Semi-integer and semi-continuous variables
-
-Semi-continuous variables are constrained to the set
-``x \in \{0\} \cup [l, u]``.
-
-Create a semi-continuous variable using the [`Semicontinuous`](@ref) set:
-```jldoctest
-julia> model = Model();
-
-julia> @variable(model, x);
-
-julia> @constraint(model, x in Semicontinuous(1.5, 3.5))
-x in MathOptInterface.Semicontinuous{Float64}(1.5, 3.5)
-```
-
-Semi-integer variables  are constrained to the set
-``x \in \{0\} \cup \{l, l+1, \dots, u\}``.
-
-Create a semi-integer variable using the [`Semiinteger`](@ref) set:
-```jldoctest
-julia> model = Model();
-
-julia> @variable(model, x);
-
-julia> @constraint(model, x in Semiinteger(1.0, 3.0))
-x in MathOptInterface.Semiinteger{Float64}(1.0, 3.0)
-```
-
 ## Special Ordered Sets of Type 1
 
 In a Special Ordered Set of Type 1 (often denoted SOS-I or SOS1), at most one

docs/src/manual/variables.md

@@ -640,6 +640,30 @@ julia> set_integer(x)
     in the model, returning a function that can be called to undo the operation
     later on.
 
+## Semi-integer and semi-continuous variables
+
+Semi-continuous variables are constrained to the set
+``x \in \{0\} \cup [l, u]``.
+
+Create a semi-continuous variable using the [`Semicontinuous`](@ref) set:
+```jldoctest
+julia> model = Model();
+
+julia> @variable(model, x in Semicontinuous(1.5, 3.5))
+x
+```
+
+Semi-integer variables  are constrained to the set
+``x \in \{0\} \cup \{l, l+1, \dots, u\}``.
+
+Create a semi-integer variable using the [`Semiinteger`](@ref) set:
+```jldoctest
+julia> model = Model();
+
+julia> @variable(model, x in Semiinteger(1.0, 3.0))
+x
+```
+
 ## Start values
 
 There are two ways to provide a primal starting solution (also called MIP-start

docs/src/tutorials/linear/tips_and_tricks.jl

@@ -237,15 +237,6 @@ M = 100
 
 # ## Semi-continuous variables
 
-# !!! info
-#     This section uses sets from [MathOptInterface](@ref moi_documentation).
-#     By default, JuMP exports the `MOI` symbol as an alias for the
-#     MathOptInterface.jl package. We recommend making this more explicit in
-#     your code by adding the following lines:
-#     ```julia
-#     import MathOptInterface as MOI
-#     ```
-
 # A semi-continuous variable is a continuous variable between bounds $[l,u]$
 # that also can assume the value zero, that is:
 # $$x \in \{0\} \cup [l,u].$$
@@ -255,6 +246,17 @@ M = 100
 model = Model();
 @variable(model, x in Semicontinuous(1.0, 2.0))
 
+# You can also represent a semi-continuous variable using the reformulation:
+
+model = Model();
+@variable(model, x)
+@variable(model, z, Bin)
+@constraint(model, x <= 2 * z)
+@constraint(model, x >= 1 * z)
+
+# When `z = 0` the two constraints are equivalent to `0 <= x <= 0`. When `z = 1`,
+# the two constraints are equivalent to `1 <= x <= 2`.
+
 # ## Semi-integer variables
 
 # A semi-integer variable is a variable which assumes integer values between
@@ -264,6 +266,17 @@ model = Model();
 model = Model();
 @variable(model, x in Semiinteger(5.0, 10.0))
 
+# You can also represent a semi-integer variable using the reformulation:
+
+model = Model();
+@variable(model, x, Int)
+@variable(model, z, Bin)
+@constraint(model, x <= 10 * z)
+@constraint(model, x >= 5 * z)
+
+# When `z = 0` the two constraints are equivalent to `0 <= x <= 0`. When `z = 1`,
+# the two constraints are equivalent to `5 <= x <= 10`.
+
 # ## Special Ordered Sets of Type 1
 
 # A Special Ordered Set of Type 1 is a set of variables, at most one of which