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Fix optimality measure in LMTR #223

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Fix optimality measure in LMTR #223

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d1d2b78
solve for LMTR optimality measure
MaxenceGollier Sep 23, 2025
174d273
print out optimality measure correctly
MaxenceGollier Sep 24, 2025
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8 changes: 5 additions & 3 deletions src/LMTR_alg.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -134,6 +134,7 @@ function LMTR(
found_σ || error("operator norm computation failed")
α⁻¹Δ⁻¹ = 1 / (α * Δk)
ν = 1 / (α⁻¹Δ⁻¹ + σmax^2 * (α⁻¹Δ⁻¹ + 1)) # ‖J'J‖ = ‖J‖²
sqrt_ξ1_νInv = one(eltype(xk))

mν∇fk = -∇fk * ν

Expand Down Expand Up @@ -178,14 +179,15 @@ function LMTR(
prox!(s, ψ, mν∇fk, ν)
ξ1 = fk + hk - mk1(s) + max(1, abs(fk + hk)) * 10 * eps()
ξ1 > 0 || error("LMTR: first prox-gradient step should produce a decrease but ξ1 = $(ξ1)")
sqrt_ξ1_νInv = ξ1 ≥ 0 ? sqrt(ξ1 / ν) : sqrt(-ξ1 / ν)

if ξ1 ≥ 0 && k == 1
ϵ_increment = ϵr * sqrt(ξ1)
ϵ_increment = ϵr * sqrt_ξ1_νInv
ϵ += ϵ_increment # make stopping test absolute and relative
ϵ_subsolver += ϵ_increment
end

if sqrt(ξ1) < ϵ
if sqrt_ξ1_νInv < ϵ
# the current xk is approximately first-order stationary
optimal = true
continue
Expand Down Expand Up @@ -276,7 +278,7 @@ function LMTR(
#! format: off
@info @sprintf "%6d %8d %8.1e %8.1e %7.1e %7.1e %8s %7.1e %7.1e %7.1e %7.1e" k 1 fk hk sqrt(ξ1) sqrt(ξ1) "" Δk χ(xk) χ(s) ν
#! format: on
@info "LMTR: terminating with √ξ1 = $(sqrt(ξ1))"
@info "LMTR: terminating with √(ξ1/ν) = $(sqrt_ξ1_νInv)"
end
end

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