change theta for better readibility

Author: MaxenceGollier

src/LMTR_alg.jl

@@ -131,7 +131,7 @@ function LMTR(
   Jt_Fk = similar(∇fk)   # temporary storage
 
   σmax = opnorm(Jk)
-  νInv = (1 + θ) * σmax^2  # ‖J'J‖ = ‖J‖²
+  νInv = σmax^2/θ  # ‖J'J‖ = ‖J‖²
 
   mν∇fk = -∇fk / νInv
 
@@ -253,7 +253,7 @@ function LMTR(
       Jk = jac_op_residual(nls, xk)
       jtprod_residual!(nls, xk, Fk, ∇fk)
       σmax = opnorm(Jk)
-      νInv = (1 + θ) * σmax^2  # ‖J'J‖ = ‖J‖²
+      νInv = σmax^2/θ  # ‖J'J‖ = ‖J‖²
       @. mν∇fk = -∇fk / νInv
     end
 

src/LM_alg.jl

@@ -124,7 +124,7 @@ function LM(
   Jt_Fk = similar(∇fk)
 
   σmax = opnorm(Jk)
-  νInv = (1 + θ) * (σmax^2 + σk)  # ‖J'J + σₖ I‖ = ‖J‖² + σₖ
+  νInv = (σmax^2 + σk)/θ  # ‖J'J + σₖ I‖ = ‖J‖² + σₖ
 
   s = zero(xk)
 
@@ -251,7 +251,7 @@ function LM(
     if ρk < η1 || ρk == Inf
       σk = σk * γ
     end
-    νInv = (1 + θ) * (σmax^2 + σk)  # ‖J'J + σₖ I‖ = ‖J‖² + σₖ
+    νInv = (σmax^2 + σk)/θ  # ‖J'J + σₖ I‖ = ‖J‖² + σₖ
     tired = k ≥ maxIter || elapsed_time > maxTime
   end
 

src/R2DH.jl

@@ -199,7 +199,7 @@ function SolverCore.solve!(
   η2::T = T(0.9),
   ν::T = eps(T)^(1 / 5),
   γ::T = T(3),
-  θ::T = eps(T)^(1 / 5),
+  θ::T = 1/(1 + eps(T)^(1 / 5)),
 ) where{T, V}
 
   reset!(stats)
@@ -275,7 +275,7 @@ function SolverCore.solve!(
   @. dkσk = D.d .+ σk
   DNorm = norm(D.d, Inf)
 
-  ν₁ = 1 / ((DNorm + σk) * (1 + θ))
+  ν₁ = θ / (DNorm + σk)
   sqrt_ξ_νInv = one(T)
 
   @. mν∇fk = -ν₁ * ∇fk
@@ -306,7 +306,7 @@ function SolverCore.solve!(
     σk = σk * γ
     dkσk .= D.d .+ σk
     DNorm = norm(D.d, Inf)
-    ν₁ = 1 / ((DNorm + σk) * (1 + θ))
+    ν₁ = θ / (DNorm + σk)
     @. mν∇fk = -ν₁ * ∇fk
     spectral_test ? prox!(s, ψ, mν∇fk, ν₁) : iprox!(s, ψ, ∇fk, dkσk)
     mks = mk(s)
@@ -399,7 +399,7 @@ function SolverCore.solve!(
     @. dkσk = D.d .+ σk
     DNorm = norm(D.d, Inf)
 
-    ν₁ = 1 / ((DNorm + σk) * (1 + θ))
+    ν₁ = θ / (DNorm + σk)
 
     @. mν∇fk = -ν₁ * ∇fk
     m_monotone > 1 && (m_fh_hist[stats.iter%(m_monotone - 1) + 1] = fk + hk)
@@ -411,7 +411,7 @@ function SolverCore.solve!(
       σk = σk * γ
       dkσk .= D.d .+ σk
       DNorm = norm(D.d, Inf)
-      ν₁ = 1 / ((DNorm + σk) * (1 + θ))
+      ν₁ = θ / (DNorm + σk)
       @. mν∇fk = -ν₁ * ∇fk
       spectral_test ? prox!(s, ψ, mν∇fk, ν₁) : iprox!(s, ψ, ∇fk, dkσk)
       mks = mk(s)
@@ -464,3 +464,8 @@ function SolverCore.solve!(
   set_residuals!(stats, zero(eltype(xk)), sqrt_ξ_νInv)
   return stats
 end
+
+
+#theta 0.000740095979741405
+#nu1 0.0003700479898707025
+#original 0.4996302256786179

src/R2N.jl

@@ -130,7 +130,7 @@ For advanced usage, first define a solver "R2NSolver" to preallocate the memory
 - `η2::T = T(0.9)`: very successful iteration threshold;
 - `ν::T = eps(T)^(1 / 5)`: inverse of the initial regularization parameter: ν = 1/σ;
 - `γ::T = T(3)`: regularization parameter multiplier, σ := σ/γ when the iteration is very successful and σ := σγ when the iteration is unsuccessful.
-- `θ::T = eps(T)^(1/5)`: is the model decrease fraction with respect to the decrease of the Cauchy model. 
+- `θ::T = 1/(1 + eps(T)^(1 / 5))`: is the model decrease fraction with respect to the decrease of the Cauchy model. 
 - `m_monotone::Int = 1`: monotonicity parameter. By default, R2DH is monotone but the non-monotone variant will be used if `m_monotone > 1`
 
 The algorithm stops either when `√(ξₖ/νₖ) < atol + rtol*√(ξ₀/ν₀) ` or `ξₖ < 0` and `√(-ξₖ/νₖ) < neg_tol` where ξₖ := f(xₖ) + h(xₖ) - φ(sₖ; xₖ) - ψ(sₖ; xₖ), and √(ξₖ/νₖ) is a stationarity measure.
@@ -212,7 +212,7 @@ function SolverCore.solve!(
   ν::T = eps(T)^(1 / 5),
   γ::T = T(3),
   β::T = 1 / eps(T),
-  θ::T = eps(T)^(1 / 5),
+  θ::T = 1/(1+eps(T)^(1 / 5)),
   kwargs...
 ) where{T, V, G}
   reset!(stats)
@@ -289,7 +289,7 @@ function SolverCore.solve!(
 
   λmax = opnorm(solver.subpb.model.B)
 
-  ν₁ = 1 / ((λmax + σk) * (1 + θ))
+  ν₁ = θ / (λmax + σk)
   ν_sub = ν₁
 
   sqrt_ξ1_νInv = one(T)
@@ -435,7 +435,7 @@ function SolverCore.solve!(
       σk = σk * γ
     end
 
-    ν₁ = 1 / ((λmax + σk) * (1 + θ))
+    ν₁ = θ / (λmax + σk)
     m_monotone > 1 && (m_fh_hist[stats.iter%(m_monotone - 1) + 1] = fk + hk)
 
     set_objective!(stats, fk + hk)

src/input_struct.jl

@@ -34,7 +34,7 @@ mutable struct ROSolverOptions{R}
     α::R = 1 / eps(R),
     ν::R = eps(R)^(1 / 5),
     γ::R = R(3),
-    θ::R = eps(R)^(1 / 5),
+    θ::R = 1/(1+eps(R)^(1 / 5)),
     β::R = 1 / eps(R),
     reduce_TR::Bool = true,
   ) where {R <: Real}