Minres Fail to solve subproblem and cuases R2N solver to Max_timed

We are using Krylov as a subsolver for R2N, you can access it https://github.com/Farhad-phd/JSOSolvers.jl.git#R2N_R2NLS_2026_Jan Here is the code that shows ```julia using Revise using JSOSolvers using HSL using Arpack, TSVD, GenericLinearAlgebra using SparseArrays, LinearAlgebra using ADNLPModels, Krylov, LinearOperators, NLPModels, NLPModelsModifiers, SolverCore using Printf using CUTEst # 1. Define the Problem n = 30 nlp = ADNLPModel( x -> sum(100 * (x[i + 1] - x[i]^2)^2 + (x[i] - 1)^2 for i = 1:(n - 1)), collect(1:n) ./ (n + 1), name = "Extended Rosenbrock", ) println("\nSubsolver = Minres, NPC Handler = AG") stats_minres = R2N(nlp; verbose = 1, max_iter = 50, subsolver = MinresR2NSubsolver, npc_handler = :ag, subsolver_verbose = 1) println("\nSubsolver = CR, NPC Handler = AG") stats_cr = R2N(nlp; verbose = 1, max_iter = 200, subsolver = CRR2NSubsolver, npc_handler = :ag, subsolver_verbose = 1) println("\nSubsolver = MinresQlp, NPC Handler = AG") stats_minres_qlp = R2N(nlp; verbose = 1, max_iter = 50, subsolver = MinresQlpR2NSubsolver, npc_handler = :ag, subsolver_verbose = 1) println("\nStastics Summary:") println("stats_minres: ", stats_minres) println("stats_cr: ", stats_cr) println("stats_minres_qlp: ", stats_minres_qlp) ``` Here is the results: ``` Stastics Summary: stats_minres: Generic Execution stats status: maximum iteration objective value: 68.38758422768275 primal feasibility: 0.0 dual feasibility: 25.73140889343297 solution: [0.9889333207366354 0.9769356894569213 0.9521497483850498 0.899043128944154 ⋯ 0.9478308012350751] iterations: 51 elapsed time: 0.3819999694824219 stats_minres_qlp: Generic Execution stats status: first-order stationary objective value: 8.264512926113936e-15 primal feasibility: 0.0 dual feasibility: 9.208909843275436e-8 solution: [1.0000000000023905 1.0000000000024127 1.0000000000013747 1.0000000000012088 ⋯ 0.9999998422126554] iterations: 35 elapsed time: 0.0280001163482666 ``` here is the first 5 iteration of the R2N with subsolver verbose = 1 ``` Subsolver = Minres, NPC Handler = AG [ Info: iter f(x) ‖∇f‖ ‖s‖ σ ρ subiter dir [ Info: 0 1.5e+02 7.6e+01 0.0e+00 8.4e-01 0.0e+00 0 MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 7.6e+01 0.0e+00 7.6e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 7.4e+01 1.4e+04 1.8e+02 2.7e-01 9.6e-01 2.0e+02 1.0e+00 3.4e+00 9.2e-01 0.18s [ Info: 1 1.4e+02 7.3e+01 1.1e-01 4.2e-01 1.0e+00 1 ↘ found approximate minimum least-squares solution MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 7.3e+01 0.0e+00 7.3e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 7.2e+01 1.0e+04 1.4e+02 1.9e-01 9.8e-01 1.6e+02 1.0e+00 4.5e+00 8.8e-01 0.00s [ Info: 2 1.3e+02 7.1e+01 1.0e-01 2.1e-01 1.0e+00 1 ↘ found approximate minimum least-squares solution MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 7.1e+01 0.0e+00 7.1e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 7.0e+01 9.3e+03 1.3e+02 2.0e-01 9.8e-01 1.5e+02 1.0e+00 4.3e+00 8.8e-01 0.00s [ Info: 3 1.3e+02 6.9e+01 1.1e-01 1.0e-01 1.0e+00 1 ↘ found approximate minimum least-squares solution MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 6.9e+01 0.0e+00 6.9e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 6.7e+01 1.1e+04 1.5e+02 2.2e-01 9.8e-01 1.7e+02 1.0e+00 4.1e+00 9.2e-01 0.00s [ Info: 4 1.2e+02 6.6e+01 9.6e-02 5.2e-02 1.0e+00 1 ↘ found approximate minimum least-squares solution MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 6.6e+01 0.0e+00 6.6e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 6.4e+01 1.2e+04 1.7e+02 2.4e-01 9.7e-01 1.9e+02 1.0e+00 3.8e+00 9.4e-01 0.00s [ Info: 5 1.1e+02 6.4e+01 9.0e-02 2.6e-02 1.0e+00 1 ↘ found approximate minimum least-squares solution MINRES: system of size 30 k ‖r‖ ‖Aᴴr‖ β cos sin ‖A‖ κ(A) test1 test2 timer 0 6.4e+01 0.0e+00 6.4e+01 -1.0e+00 0.0e+00 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.00s 1 6.2e+01 1.3e+04 1.9e+02 2.6e-01 9.7e-01 2.1e+02 1.0e+00 3.6e+00 9.5e-01 0.00s [ Info: 6 1.1e+02 6.1e+01 8.3e-02 1.3e-02 1.0e+00 1 ↘ found approximate minimum least-squares solution Subsolver = CR, NPC Handler = AG [ Info: iter f(x) ‖∇f‖ ‖s‖ σ ρ subiter dir [ Info: 0 1.5e+02 7.6e+01 0.0e+00 8.4e-01 0.0e+00 0 [ Info: 1 1.0e+02 1.0e+02 1.1e+00 1.3e+00 5.3e-01 2 ↘ nonpositive curvature [ Info: 2 9.7e+01 1.3e+02 7.4e-01 1.9e+00 2.7e-01 10 ↘ nonpositive curvature [ Info: 3 7.7e+01 1.7e+01 3.9e-01 9.4e-01 9.9e-01 6 ↘ solution good enough given atol and rtol [ Info: 4 7.6e+01 2.1e+01 2.3e-01 1.4e+00 7.4e-01 7 ↘ nonpositive curvature [ Info: 5 7.6e+01 1.9e+01 4.1e-01 2.1e+00 2.4e-01 11 ↘ solution good enough given atol and rtol [ Info: 6 7.5e+01 3.1e+01 3.1e-01 3.2e+00 4.7e-01 6 ↘ nonpositive curvature Subsolver = MinresQlp, NPC Handler = AG [ Info: iter f(x) ‖∇f‖ ‖s‖ σ ρ subiter dir [ Info: 0 1.5e+02 7.6e+01 0.0e+00 8.4e-01 0.0e+00 0 MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 7.6e+01 ✗ ✗ ✗ ✗ 7.6e+01 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 7.4e+01 1.4e+04 1.8e+02 1.9e+02 1.9e+02 2.0e+02 1.0e+00 Inf 0.00s 2 7.3e+01 9.3e+03 4.5e+02 4.5e+02 -9.8e+01 9.6e+02 8.6e+00 Inf 0.00s nonpositive curvature detected: cₖ * λbarₖ = 5.197591e+00 [ Info: 1 1.0e+02 1.0e+02 1.1e+00 1.3e+00 5.3e-01 3 ↘ nonpositive curvature MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 1.0e+02 ✗ ✗ ✗ ✗ 1.0e+02 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 6.4e+01 6.9e+04 4.0e+02 6.6e+02 6.6e+02 6.7e+02 1.0e+00 Inf 0.00s 2 4.6e+01 3.7e+04 4.7e+02 6.5e+02 -4.0e+02 1.3e+03 2.7e+00 Inf 0.00s 3 3.9e+01 3.0e+04 6.9e+02 8.2e+02 -3.4e+02 1.8e+03 3.3e+00 2.8e-01 0.00s 4 3.6e+01 1.2e+04 4.6e+02 4.9e+02 -2.0e+02 2.3e+03 5.7e+00 1.3e-01 0.00s 5 3.4e+01 6.8e+03 3.8e+02 4.0e+02 -9.1e+01 2.6e+03 1.2e+01 7.1e-02 0.00s 6 3.1e+01 8.8e+03 4.8e+02 5.3e+02 -5.6e+01 2.8e+03 2.0e+01 4.9e-02 0.00s 7 2.8e+01 9.9e+03 5.1e+02 5.6e+02 -4.4e+01 3.1e+03 2.5e+01 3.8e-02 0.00s 8 2.5e+01 8.3e+03 4.4e+02 5.0e+02 -4.1e+01 3.3e+03 2.7e+01 3.0e-02 0.00s 9 2.4e+01 6.8e+03 4.8e+02 5.0e+02 -4.9e+01 3.4e+03 2.7e+01 2.5e-02 0.00s 10 2.4e+01 3.8e+03 4.6e+02 4.6e+02 -8.2e+01 3.6e+03 2.7e+01 2.1e-02 0.00s nonpositive curvature detected: cₖ * λbarₖ = 6.161692e+00 [ Info: 2 9.7e+01 1.3e+02 7.4e-01 1.9e+00 2.7e-01 11 ↘ nonpositive curvature MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 1.3e+02 ✗ ✗ ✗ ✗ 1.3e+02 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 6.6e+01 8.8e+04 3.6e+02 6.9e+02 6.9e+02 7.0e+02 1.0e+00 Inf 0.00s 2 3.7e+01 4.8e+04 4.3e+02 7.6e+02 -5.0e+02 1.3e+03 2.1e+00 Inf 0.00s 3 2.4e+01 3.2e+04 6.1e+02 9.3e+02 -4.9e+02 1.9e+03 2.2e+00 1.3e-01 0.00s 4 1.8e+01 1.5e+04 5.4e+02 7.2e+02 -3.7e+02 2.3e+03 2.9e+00 4.8e-02 0.00s 5 1.3e+01 8.8e+03 4.2e+02 5.8e+02 -2.3e+02 2.6e+03 4.7e+00 2.2e-02 0.00s 6 8.7e+00 6.1e+03 3.5e+02 5.3e+02 -1.7e+02 2.8e+03 6.2e+00 1.1e-02 0.00s [ Info: 3 7.7e+01 1.7e+01 3.9e-01 9.4e-01 9.9e-01 6 ↘ solution good enough given atol and rtol MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 1.7e+01 ✗ ✗ ✗ ✗ 1.7e+01 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 1.2e+01 1.2e+04 4.8e+02 7.0e+02 7.0e+02 7.0e+02 1.0e+00 Inf 0.00s 2 7.7e+00 6.7e+03 4.3e+02 6.5e+02 -3.4e+02 1.5e+03 3.9e+00 Inf 0.00s 3 5.3e+00 4.4e+03 4.3e+02 6.3e+02 -2.7e+02 1.8e+03 5.0e+00 3.2e-01 0.00s 4 4.1e+00 3.5e+03 6.2e+02 7.9e+02 -2.9e+02 2.2e+03 5.0e+00 9.1e-02 0.00s 5 3.8e+00 1.2e+03 3.9e+02 4.2e+02 -1.9e+02 2.5e+03 7.1e+00 4.9e-02 0.00s 6 3.7e+00 6.1e+02 3.3e+02 3.5e+02 -9.1e+01 2.7e+03 1.5e+01 2.7e-02 0.00s 7 3.7e+00 5.8e+02 5.1e+02 5.2e+02 -9.2e+01 2.8e+03 1.5e+01 2.2e-02 0.00s nonpositive curvature detected: cₖ * λbarₖ = 2.180380e+00 [ Info: 4 7.6e+01 2.1e+01 2.3e-01 1.4e+00 7.4e-01 8 ↘ nonpositive curvature MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 2.1e+01 ✗ ✗ ✗ ✗ 2.1e+01 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 1.4e+01 1.6e+04 4.9e+02 7.7e+02 7.7e+02 7.7e+02 1.0e+00 Inf 0.00s 2 8.6e+00 8.2e+03 4.2e+02 6.6e+02 -3.9e+02 1.5e+03 3.4e+00 Inf 0.00s 3 5.0e+00 5.8e+03 4.2e+02 7.3e+02 -3.1e+02 1.9e+03 4.3e+00 2.2e-01 0.00s 4 3.8e+00 3.7e+03 6.4e+02 8.3e+02 -3.9e+02 2.2e+03 4.3e+00 7.2e-02 0.00s 5 3.6e+00 1.1e+03 3.9e+02 4.2e+02 -2.2e+02 2.5e+03 6.1e+00 3.7e-02 0.00s 6 3.5e+00 4.4e+02 2.9e+02 3.0e+02 -7.8e+01 2.7e+03 1.7e+01 2.2e-02 0.00s 7 3.4e+00 6.4e+02 4.6e+02 4.9e+02 -4.3e+01 2.9e+03 3.1e+01 1.7e-02 0.00s 8 3.2e+00 7.0e+02 4.9e+02 5.1e+02 -3.5e+01 3.1e+03 3.9e+01 1.5e-02 0.00s 9 2.5e+00 8.0e+02 3.1e+02 3.8e+02 -1.6e+01 3.4e+03 8.6e+01 1.1e-02 0.00s 10 1.8e+00 7.6e+02 2.6e+02 3.6e+02 -1.6e+01 3.5e+03 8.6e+01 7.4e-03 0.00s 11 1.1e+00 7.8e+02 3.0e+02 4.8e+02 -2.0e+01 3.6e+03 8.6e+01 4.4e-03 0.00s [ Info: 5 7.6e+01 1.9e+01 4.1e-01 2.1e+00 2.4e-01 11 ↘ solution good enough given atol and rtol MINRES-QLP: system of size 30 k ‖rₖ‖ ‖Arₖ₋₁‖ βₖ₊₁ Rₖ.ₖ Lₖ.ₖ ‖A‖ κ(A) backward timer 0 1.9e+01 ✗ ✗ ✗ ✗ 1.9e+01 ✗ ✗ ✗ ✗ ✗ ✗ ✗ ✗ 0.0e+00 0.0e+00 ✗ ✗ ✗ ✗ 0.00s 1 1.2e+01 6.0e+03 2.0e+02 3.2e+02 3.2e+02 3.2e+02 1.0e+00 Inf 0.00s 2 8.6e+00 5.9e+03 4.1e+02 5.6e+02 -2.7e+02 8.7e+02 2.5e+00 Inf 0.00s 3 6.5e+00 3.2e+03 3.4e+02 4.4e+02 -1.9e+02 1.3e+03 3.8e+00 2.6e-01 0.00s 4 5.2e+00 3.6e+03 5.6e+02 7.0e+02 -1.8e+02 1.7e+03 3.9e+00 7.5e-02 0.00s 5 5.0e+00 1.8e+03 5.1e+02 5.3e+02 -2.0e+02 2.0e+03 4.3e+00 4.7e-02 0.00s 6 5.0e+00 5.7e+02 3.9e+02 3.9e+02 -1.1e+02 2.3e+03 7.2e+00 3.1e-02 0.00s nonpositive curvature detected: cₖ * λbarₖ = 1.964178e+00 [ Info: 6 7.5e+01 3.1e+01 3.1e-01 3.2e+00 4.7e-01 7 ↘ nonpositive curvature ```