From c561d8bdc73d7362743d34f9096e77d6673d9442 Mon Sep 17 00:00:00 2001
From: MohamedLaghdafHABIBOULLAH
 <81633807+MohamedLaghdafHABIBOULLAH@users.noreply.github.com>
Date: Tue, 2 Aug 2022 01:57:07 -0400
Subject: [PATCH 1/3] Update R2_alg.jl
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

To take into account the case where ξ is small and negative.
---
 src/R2_alg.jl | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/src/R2_alg.jl b/src/R2_alg.jl
index 91c54543..99364e95 100644
--- a/src/R2_alg.jl
+++ b/src/R2_alg.jl
@@ -71,7 +71,8 @@ function R2(
   h::H,
   options::ROSolverOptions,
   x0::AbstractVector,
-) where {F <: Function, G <: Function, H}
+  T::R,
+) where {F <: Function, G <: Function, H, R <: Real}
   start_time = time()
   elapsed_time = 0.0
   ϵ = options.ϵ
@@ -146,9 +147,9 @@ function R2(
     Complex_hist[k] += 1
     mks = mk(s)
     ξ = hk - mks + max(1, abs(hk)) * 10 * eps()
-    ξ > 0 || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
+    ξ > T || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
 
-    if sqrt(ξ) < ϵ
+    if sqrt(abs(T)) <= sqrt(abs(ξ)) < ϵ
       optimal = true
       continue
     end
@@ -165,7 +166,7 @@ function R2(
 
     if (verbose > 0) && (k % ptf == 0)
       #! format: off
-      @info @sprintf "%6d %8.1e %8.1e %7.1e %8.1e %7.1e %7.1e %7.1e %1s" k fk hk sqrt(ξ) ρk σk norm(xk) norm(s) σ_stat
+      @info @sprintf "%6d %8.1e %8.1e %7.1e %8.1e %7.1e %7.1e %7.1e %1s" k fk hk sqrt(abs(ξ)) ρk σk norm(xk) norm(s) σ_stat
       #! format: on
     end
 
@@ -197,7 +198,7 @@ function R2(
       @info @sprintf "%6d %8.1e %8.1e" k fk hk
     elseif optimal
       #! format: off
-      @info @sprintf "%6d %8.1e %8.1e %7.1e %8s %7.1e %7.1e %7.1e" k fk hk sqrt(ξ) "" σk norm(xk) norm(s)
+      @info @sprintf "%6d %8.1e %8.1e %7.1e %8s %7.1e %7.1e %7.1e" k fk hk sqrt(abs(ξ)) "" σk norm(xk) norm(s)
       #! format: on
       @info "R2: terminating with √ξ = $(sqrt(ξ))"
     end

From c79049f3ae710d9f88ee1f55967735a9bba29471 Mon Sep 17 00:00:00 2001
From: MohamedLaghdafHABIBOULLAH
 <81633807+MohamedLaghdafHABIBOULLAH@users.noreply.github.com>
Date: Thu, 4 Aug 2022 03:00:22 -0400
Subject: [PATCH 2/3] Update R2_alg.jl

---
 src/R2_alg.jl | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/R2_alg.jl b/src/R2_alg.jl
index 99364e95..cc5da1d9 100644
--- a/src/R2_alg.jl
+++ b/src/R2_alg.jl
@@ -53,7 +53,7 @@ function R2(nlp::AbstractNLPModel, args...; kwargs...)
     nlp,
     solution = xk,
     objective = outdict[:fk] + outdict[:hk],
-    dual_feas = sqrt(outdict[:ξ]),
+    dual_feas = sqrt(abs(outdict[:ξ])),
     iter = k,
     elapsed_time = outdict[:elapsed_time],
     solver_specific = Dict(
@@ -69,9 +69,9 @@ function R2(
   f::F,
   ∇f!::G,
   h::H,
-  options::ROSolverOptions,
-  x0::AbstractVector,
-  T::R,
+  options::ROSolverOptions{R},
+  x0::AbstractVector{R},
+  neg_tol::R = -eps(R)^(1/3) ,
 ) where {F <: Function, G <: Function, H, R <: Real}
   start_time = time()
   elapsed_time = 0.0
@@ -84,6 +84,7 @@ function R2(
   η2 = options.η2
   ν = options.ν
   γ = options.γ
+  neg_tol < 0 || error("neg_tol must be negative")
 
   if verbose == 0
     ptf = Inf
@@ -147,9 +148,9 @@ function R2(
     Complex_hist[k] += 1
     mks = mk(s)
     ξ = hk - mks + max(1, abs(hk)) * 10 * eps()
-    ξ > T || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
+    ξ > neg_tol || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
 
-    if sqrt(abs(T)) <= sqrt(abs(ξ)) < ϵ
+    if  sqrt(abs(ξ)) < max(ϵ, abs(neg_tol))
       optimal = true
       continue
     end
@@ -200,7 +201,7 @@ function R2(
       #! format: off
       @info @sprintf "%6d %8.1e %8.1e %7.1e %8s %7.1e %7.1e %7.1e" k fk hk sqrt(abs(ξ)) "" σk norm(xk) norm(s)
       #! format: on
-      @info "R2: terminating with √ξ = $(sqrt(ξ))"
+      @info "R2: terminating with √ξ = $(sqrt(abs(ξ)))"
     end
   end
 

From d00ebdc6be29d3b7bc530dd72c8b028d66e3ef4f Mon Sep 17 00:00:00 2001
From: MohamedLaghdafHABIBOULLAH
 <81633807+MohamedLaghdafHABIBOULLAH@users.noreply.github.com>
Date: Mon, 8 Aug 2022 19:35:38 -0400
Subject: [PATCH 3/3] Update R2_alg.jl

---
 src/R2_alg.jl | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/R2_alg.jl b/src/R2_alg.jl
index cc5da1d9..d23e4b0c 100644
--- a/src/R2_alg.jl
+++ b/src/R2_alg.jl
@@ -53,7 +53,7 @@ function R2(nlp::AbstractNLPModel, args...; kwargs...)
     nlp,
     solution = xk,
     objective = outdict[:fk] + outdict[:hk],
-    dual_feas = sqrt(abs(outdict[:ξ])),
+    dual_feas = sqrt(outdict[:ξ]),
     iter = k,
     elapsed_time = outdict[:elapsed_time],
     solver_specific = Dict(
@@ -148,13 +148,14 @@ function R2(
     Complex_hist[k] += 1
     mks = mk(s)
     ξ = hk - mks + max(1, abs(hk)) * 10 * eps()
-    ξ > neg_tol || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
-
-    if  sqrt(abs(ξ)) < max(ϵ, abs(neg_tol))
+    
+    if neg_tol <= ξ <= ϵ^2
       optimal = true
+      ξ = abs(ξ)
       continue
     end
 
+    ξ > 0 || error("R2: prox-gradient step should produce a decrease but ξ = $(ξ)")
     xkn .= xk .+ s
     fkn = f(xkn)
     hkn = h(xkn)
@@ -167,7 +168,7 @@ function R2(
 
     if (verbose > 0) && (k % ptf == 0)
       #! format: off
-      @info @sprintf "%6d %8.1e %8.1e %7.1e %8.1e %7.1e %7.1e %7.1e %1s" k fk hk sqrt(abs(ξ)) ρk σk norm(xk) norm(s) σ_stat
+      @info @sprintf "%6d %8.1e %8.1e %7.1e %8.1e %7.1e %7.1e %7.1e %1s" k fk hk sqrt(ξ) ρk σk norm(xk) norm(s) σ_stat
       #! format: on
     end
 
@@ -199,9 +200,9 @@ function R2(
       @info @sprintf "%6d %8.1e %8.1e" k fk hk
     elseif optimal
       #! format: off
-      @info @sprintf "%6d %8.1e %8.1e %7.1e %8s %7.1e %7.1e %7.1e" k fk hk sqrt(abs(ξ)) "" σk norm(xk) norm(s)
+      @info @sprintf "%6d %8.1e %8.1e %7.1e %8s %7.1e %7.1e %7.1e" k fk hk sqrt(ξ) "" σk norm(xk) norm(s)
       #! format: on
-      @info "R2: terminating with √ξ = $(sqrt(abs(ξ)))"
+      @info "R2: terminating with √ξ = $(sqrt(ξ))"
     end
   end