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

Author: MohamedLaghdafHABIBOULLAH

src/shiftedNormL0.jl

@@ -67,13 +67,17 @@ 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
+    if d[i] ≤ 0
+      y[i] = - 1/eps(R) 
+      continue
+    else 
+      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
+      end
     end
   end
   return y

src/shiftedNormL1.jl

@@ -67,8 +67,12 @@ 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])
+    if d[i] < 0
+      y[i] = - 1/eps(R) 
+      continue
+    else 
+      y[i] = min(max(y[i], -g[i] / d[i] - λ / d[i]), -g[i] / d[i] + λ / d[i])
+    end
   end
 
   return y

test/partial_prox.jl

@@ -58,7 +58,6 @@ 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))
       for d ∈ [ones(n), 2 * ones(n)]
         y = iprox(ψ, q, d)
         σ = d[1]