compute_As_slope_qs! Function

src/auxiliary/bounds.jl

@@ -1,6 +1,6 @@
 # Auxiliary function related to bound-constrainted problems
 
-export active, active!, breakpoints, compute_Hs_slope_qs!, project!, project_step!
+export active, active!, breakpoints, compute_Hs_slope_qs!, compute_As_slope_qs!, project!, project_step!
 
 """
     active(x, ℓ, u; rtol = 1e-8, atol = 1e-8)
@@ -110,6 +110,23 @@ function compute_Hs_slope_qs!(
   return slope, qs
 end
 
+"""
+    slope, qs = compute_As_slope_qs!(As, A, s, Fx)
+
+Compute `slope = dot(As, Fx)` and `qs = dot(As, As) / 2 + slope`. Use `As` to store `A * s`.
+"""
+function compute_As_slope_qs!(
+  As::AbstractVector{T},
+  A::Union{AbstractMatrix, AbstractLinearOperator},
+  s::AbstractVector{T},
+  Fx::AbstractVector{T},
+) where {T <: Real}
+  mul!(As, A, s)
+  slope = dot(As, Fx)
+  qs = dot(As, As) / 2 + slope
+  return slope, qs
+end
+
 """
     project!(y, x, ℓ, u)
 

test/test_auxiliary.jl

@@ -46,6 +46,16 @@ function test_auxiliary()
     a = @allocated compute_Hs_slope_qs!(Hx, H, x, g)
     @test a == 0
 
+    x1 = [10.0; 11.0; 12.0; 13.0; 14.0; 15.0; 16.0]
+    A = diagm(0 => 2 * ones(7), -1 => -ones(6), 1 => -ones(6))
+    As = zeros(7)
+    Fx = rand(7)
+    slope, qx = compute_As_slope_qs!(As, A, x1, Fx)
+    @test slope == dot(As, Fx)
+    @test qx == dot(As, As) / 2 + slope
+    b = @allocated compute_As_slope_qs!(As, A, x1, Fx)
+    @test b == 0
+
     z = [ℓ[1:2] - rand(2); x[3]; u[4:5] + rand(2)]
     y = rand(5)
     project!(y, z, ℓ, u)