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update LM solver #156

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MohamedLaghdafHABIBOULLAH
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We enable the use of R2DH as a subsolver with different stopping criteria for the subproblem.
Remark: this PR uses the input_struct.jl defined here: #153

@MohamedLaghdafHABIBOULLAH
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@dpo pour cette PR j'ai modifié le critère d'arrêt du sous solveur de LM pour qu'il soit le même que R2N

@@ -176,22 +179,24 @@ function LM(
prox!(s, ψ, ∇fk, ν)
ξ1 = fk + hk - mk1(s) + max(1, abs(fk + hk)) * 10 * eps() # TODO: isn't mk(s) returned by subsolver?
ξ1 > 0 || error("LM: first prox-gradient step should produce a decrease but ξ1 = $(ξ1)")
sqrt_ξ1_νInv = ξ1 > 0 ? sqrt(ξ1 * νInv) : 10.
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?????

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Comment on lines +252 to +254
if nonlinear == true
σmax = opnorm(Jk)
end
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Suggested change
if nonlinear == true
σmax = opnorm(Jk)
end
if nonlinear
σmax = opnorm(Jk)
end

@@ -252,6 +260,7 @@ function LM(
σk = σk * γ
end
νInv = (1 + θ) * (σmax^2 + σk) # ‖J'J + σₖ I‖ = ‖J‖² + σₖ

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