From 394725dbb60261445021e69c9e0d786fe5f33fc6 Mon Sep 17 00:00:00 2001
From: MohamedLaghdafHABIBOULLAH <mohamed-laghdaf-2.habiboullah@polymtl.ca>
Date: Tue, 17 Sep 2024 01:55:03 -0400
Subject: [PATCH 1/2] generalization of iprox for L0 and L1 norm if D is not
 positive

---
 src/shiftedNormL0.jl | 18 +++++++++++-------
 src/shiftedNormL1.jl |  8 ++++++--
 test/partial_prox.jl |  1 -
 3 files changed, 17 insertions(+), 10 deletions(-)

diff --git a/src/shiftedNormL0.jl b/src/shiftedNormL0.jl
index 38be69d2..f817ac9b 100644
--- a/src/shiftedNormL0.jl
+++ b/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
diff --git a/src/shiftedNormL1.jl b/src/shiftedNormL1.jl
index af89b210..e2d23fc3 100644
--- a/src/shiftedNormL1.jl
+++ b/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
diff --git a/test/partial_prox.jl b/test/partial_prox.jl
index e7e5b2ff..bef783d7 100644
--- a/test/partial_prox.jl
+++ b/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]

From b6711dfa410ce796a2a95cb21e645d100cd9d621 Mon Sep 17 00:00:00 2001
From: MohamedLaghdafHABIBOULLAH <mohamed-laghdaf-2.habiboullah@polymtl.ca>
Date: Sat, 22 Feb 2025 07:32:54 -0500
Subject: [PATCH 2/2] Add the special cases for di<0 and di=0, along with
 corresponding test

---
 src/shiftedNormL0.jl | 16 +++++++++++-----
 src/shiftedNormL1.jl | 13 +++++++++----
 test/partial_prox.jl | 17 ++++++++++++++++-
 3 files changed, 36 insertions(+), 10 deletions(-)

diff --git a/src/shiftedNormL0.jl b/src/shiftedNormL0.jl
index f817ac9b..425ec365 100644
--- a/src/shiftedNormL0.jl
+++ b/src/shiftedNormL0.jl
@@ -67,16 +67,22 @@ function iprox!(
   λ = ψ.h.lambda
   for i ∈ eachindex(y)
     di = d[i]
-    if d[i] ≤ 0
-      y[i] = - 1/eps(R) 
-      continue
+    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 - g[i]) ≤ ci
+      if abs(di * xps - gi) ≤ ci
         y[i] = -xps
       else
-        y[i] = -g[i] / di
+        y[i] = -gi / di
       end
     end
   end
diff --git a/src/shiftedNormL1.jl b/src/shiftedNormL1.jl
index e2d23fc3..22ab1b75 100644
--- a/src/shiftedNormL1.jl
+++ b/src/shiftedNormL1.jl
@@ -67,11 +67,16 @@ function iprox!(
   @. y = -ψ.xk - ψ.sj
 
   for i ∈ eachindex(y)
-    if d[i] < 0
-      y[i] = - 1/eps(R) 
-      continue
+    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], -g[i] / d[i] - λ / d[i]), -g[i] / d[i] + λ / d[i])
+      y[i] = min(max(y[i], -gi / di - λ / di), -gi / di + λ / di)
     end
   end
 
diff --git a/test/partial_prox.jl b/test/partial_prox.jl
index bef783d7..bf353a40 100644
--- a/test/partial_prox.jl
+++ b/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)
@@ -58,6 +59,7 @@ for op ∈ (:NormL0, :NormL1, :RootNormLhalf)
     # tests iprox without bounds
     if op == :NormL0 || op == :NormL1
       ψ = shifted(h, x)
+      # test iprox with d > 0
       for d ∈ [ones(n), 2 * ones(n)]
         y = iprox(ψ, q, d)
         σ = d[1]
@@ -68,6 +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