generalization of iprox for L0 and L1 norm if D is not positive

src/shiftedNormL0.jl

@@ -67,13 +67,23 @@ function iprox!(
   λ = ψ.h.lambda
   for i ∈ eachindex(y)
     di = d[i]
-    @assert di > 0
-    ci = sqrt(2 * λ * di)
-    xps = ψ.xk[i] + ψ.sj[i]
-    if abs(di * xps - g[i]) ≤ ci
-      y[i] = -xps
-    else
-      y[i] = -g[i] / di
+    gi = g[i]
+    if di < 0
+      y[i] = -Inf
+    elseif di == 0
+      if gi == 0
+        y[i] = -ψ.xk[i] - ψ.sj[i]
+      else
+        y[i] = sign(gi) * Inf
+      end
+    else 
+      ci = sqrt(2 * λ * di)
+      xps = ψ.xk[i] + ψ.sj[i]
+      if abs(di * xps - gi) ≤ ci
+        y[i] = -xps
+      else
+        y[i] = -gi / di
+      end
     end
   end
   return y

src/shiftedNormL1.jl

@@ -67,8 +67,17 @@ function iprox!(
   @. y = -ψ.xk - ψ.sj
 
   for i ∈ eachindex(y)
-    @assert d[i] > 0
-    y[i] = min(max(y[i], -g[i] / d[i] - λ / d[i]), -g[i] / d[i] + λ / d[i])
+    di = d[i]
+    gi = g[i]
+    if di < 0
+      y[i] = -Inf
+    elseif di == 0
+      if abs(gi) > λ
+        y[i] = sign(gi) * Inf
+      end
+    else 
+      y[i] = min(max(y[i], -gi / di - λ / di), -gi / di + λ / di)
+    end
   end
 
   return y

test/partial_prox.jl

@@ -1,7 +1,8 @@
 # test partial prox feature for operators that implement it
 for op ∈ (:NormL0, :NormL1, :RootNormLhalf)
   @testset "shifted $op with box partial prox" begin
-    h = eval(op)(3.14)
+    λ = 3.14
+    h = eval(op)(λ)
     n = 5
     l = zeros(n)
     u = ones(n)
@@ -58,7 +59,7 @@ for op ∈ (:NormL0, :NormL1, :RootNormLhalf)
     # tests iprox without bounds
     if op == :NormL0 || op == :NormL1
       ψ = shifted(h, x)
-      @test_throws AssertionError iprox(ψ, q, zeros(n))
+      # test iprox with d > 0
       for d ∈ [ones(n), 2 * ones(n)]
         y = iprox(ψ, q, d)
         σ = d[1]
@@ -69,6 +70,19 @@ for op ∈ (:NormL0, :NormL1, :RootNormLhalf)
           end
         end
       end
+      # test iprox with d < 0
+      for d ∈ [-ones(n), -2 * ones(n)]
+        y = iprox(ψ, q, d)
+        @test all(isinf.(y))
+      end
+      # test iprox with d = 0
+      d = zeros(n)
+      q1 = (λ + 1) * ones(n)
+      y = iprox(ψ, q1, d)
+      @test all(isinf.(y))
+      q2 = zeros(n)
+      y = iprox(ψ, q2, d)
+      @test all(y .== -ψ.xk - ψ.sj)
     end
   end
 end