add qp-rand problem

Author: geoffroyleconte

src/qp_rand_model.jl

@@ -2,30 +2,34 @@ export qp_rand_model
 using .QuadraticModels
 
 """
-    model, x0 = qp_rand_model(n, dens = 1.0e-3)
+    model, x0 = qp_rand_model(n; dens = 1.0e-3, convex = false)
 
 Return an instance of a `QuadraticModel` representing
 
-   ½ xᵀQx + cᵀx   s.t.  x ≥ 1,
+   ½ xᵀHx + cᵀx   s.t.  l ≤ x ≤ u,
 
-where Q = A + A' + I where A is a random square matrix with density `dens`.
+with H = A + A' or H = A * A' + I (see the `convex` keyword argument) where A is a random square matrix with density `dens`, `l = -e -tₗ` and `u = e + tᵤ` where `tₗ` and `tᵤ` are sampled from a uniform distribution between 0 and 1.    
 
 ## Arguments
 
 * `n :: Int`: size of the problem,
-* `dens :: Real`: density of A used to generate the quadratic model.
+
+## Keyword arguments
+
+* `dens :: Real`: density of `A`` used to generate the quadratic model (default: `1.0e-3`).
+* `convex :: Bool`: true to generate a convex `H` (default: `false`).
 
 ## Return Value
 
-An instance of a `QuadraticModel`
+An instance of a `QuadraticModel`.
 """
-function qp_rand_model(n::Int, dens::R = 1.0e-3) where {R <: Real}
-  A = sprand(R, n, n, dens)
-  H = A + A' + I
+function qp_rand_model(n::Int; dens::R = 1.0e-4, convex::Bool = false) where {R <: Real}
+  A = sprandn(R, n, n, dens)
+  H = convex ? (A * A') : (A + A') #+ I
   c = randn(R, n)
-  l = .-ones(R, n) #-one(R) .- rand(R, n)
-  # u = one(R) .+ rand(R, n)
-  qp = QuadraticModel(c, H; lvar = l)
+  l = -one(R) .- rand(R, n)
+  u = one(R) .+ rand(R, n)
+  qp = QuadraticModel(c, H; lvar = l, uvar = u)
   x0 = zeros(R, n)
   qp, x0
 end

test/runtests.jl

@@ -154,8 +154,13 @@ end
 
 @testset "QP-rand" begin
   n, dens = 100, 0.1
-  model, x0 = qp_rand_model(n, dens)
-  @test all(model.meta.lvar .== -1.0)
-  @test all(model.meta.uvar .== Inf)
+  model, x0 = qp_rand_model(n; dens = dens, convex = false)
+  @test all(-2.0 .≤  model.meta.lvar .≤ 0.0)
+  @test all(0.0 .≤  model.meta.uvar .≤ 2.0)
+  @test all(model.meta.x0 .== x0)
+
+  model, x0 = qp_rand_model(n; dens = dens, convex = true)
+  @test all(-2.0 .≤  model.meta.lvar .≤ 0.0)
+  @test all(0.0 .≤  model.meta.uvar .≤ 2.0)
   @test all(model.meta.x0 .== x0)
 end