update theta default value

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/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}