remove nuInv in R2DH & R2N & TRDH

Author: MaxenceGollier

src/R2DH.jl

@@ -191,7 +191,7 @@ function R2DH(
   Dkσk = D.d .+ σk
   DNorm = norm(D.d, Inf)
 
-  ν = 1 / ((DNorm + σk) * (1 + θ))
+  ν = θ / (DNorm + σk)
   mν∇fk = -ν * ∇fk
   sqrt_ξ_νInv = one(R)  
 
@@ -274,7 +274,7 @@ function R2DH(
     end
 
     Dkσk .= D.d .+ σk
-    ν = 1 / ((DNorm + σk) * (1 + θ))
+    ν = θ / (DNorm + σk)
 
     tired = maxIter > 0 && k ≥ maxIter
     if !tired

src/R2N.jl

@@ -134,7 +134,7 @@ function R2N(
 
   λmax, found_λ = opnorm(Bk)
   found_λ || error("operator norm computation failed")
-  νInv = (1 + θ) * (σk + λmax)
+  ν =  θ / (σk + λmax)
   sqrt_ξ1_νInv = one(R)
 
   optimal = false
@@ -166,11 +166,11 @@ function R2N(
     # take first proximal gradient step s1 and see if current xk is nearly stationary
     # s1 minimizes φ1(s) + ‖s‖² / 2 / ν + ψ(s) ⟺ s1 ∈ prox{νψ}(-ν∇φ1(0)).
 
-    subsolver_options.ν = 1 / νInv
+    subsolver_options.ν = ν
     prox!(s, ψ, -subsolver_options.ν * ∇fk, subsolver_options.ν)
     ξ1 = hk - mk1(s) + max(1, abs(hk)) * 10 * eps()
     ξ1 > 0 || error("R2N: first prox-gradient step should produce a decrease but ξ1 = $(ξ1)")
-    sqrt_ξ1_νInv = sqrt(ξ1 * νInv)
+    sqrt_ξ1_νInv = sqrt(ξ1 / ν)
 
     if ξ1 ≥ 0 && k == 1
       ϵ_increment = ϵr * sqrt_ξ1_νInv
@@ -188,7 +188,7 @@ function R2N(
     subsolver_options.ϵa = k == 1 ? 1.0e-3 : min(sqrt_ξ1_νInv^(1.5), sqrt_ξ1_νInv * 1e-3)
     verbose > 0 && @debug "setting inner stopping tolerance to" subsolver_options.optTol
     subsolver_options.σk = σk
-    subsolver_args = subsolver == R2DH ? (SpectralGradient(νInv, f.meta.nvar),) : ()
+    subsolver_args = subsolver == R2DH ? (SpectralGradient(1 / ν, f.meta.nvar),) : ()
     s, iter, _ = with_logger(subsolver_logger) do
       subsolver(φ, ∇φ!, ψ, subsolver_args..., subsolver_options, s)
     end
@@ -256,7 +256,7 @@ function R2N(
     if ρk < η1 || ρk == Inf
         σk = σk * γ
     end
-    νInv = (1 + θ) * (σk + λmax)
+    ν = θ / (σk + λmax)
     tired = k ≥ maxIter || elapsed_time > maxTime
   end
 

src/TRDH_alg.jl

@@ -200,8 +200,7 @@ function TRDH(
   ∇f!(∇fk, xk)
   ∇fk⁻ = copy(∇fk)
   DNorm = norm(D.d, Inf)
-  νInv = DNorm + one(R) / (α * Δk)
-  ν = one(R) / νInv
+  ν = (α * Δk)/(DNorm + one(R))
   mν∇fk = -ν .* ∇fk
   sqrt_ξ_νInv = one(R)
 
@@ -318,8 +317,7 @@ function TRDH(
       has_bnds ? set_bounds!(ψ, l_bound_k, u_bound_k) : set_radius!(ψ, Δk)
     end
 
-    νInv = reduce_TR ? (DNorm + one(R) / (α * Δk)) : (DNorm + one(R) / α)
-    ν = one(R) / νInv
+    ν = reduce_TR ? (α * Δk)/(DNorm + one(R)) : α / (DNorm + one(R))
     mν∇fk .= -ν .* ∇fk
 
     tired = k ≥ maxIter || elapsed_time > maxTime