23 CUTEst problems where Ipopt succeeds but ripopt fails

[jkitchin]

Summary

37 CUTEst problems that Ipopt solves (Optimal or Acceptable) but ripopt fails on. These represent the current reliability gap and are targets for future improvement.

Failure Mode Breakdown

Mode	Count	Description
NumericalError	31	KKT factorization or solve quality too poor to continue
RestorationFailed	3	Feasibility restoration could not reduce constraint violation
MaxIterations	2	Did not converge within iteration budget
Timeout	1	Exceeded wall-time limit

Problem Characteristics

Category	Count
Small (n+m <= 20)	12
Medium (20 < n+m <= 100)	6
Large (n+m > 100)	19
Unconstrained (m=0)	11
Constrained (m>0)	26
mu stuck high (>1e-6 at termination)	12
mu reached floor (<=1e-6)	24

Detailed Results

Problem	n	m	ripopt status	pr	du	mu	iters	ipopt obj	ipopt iters
ACOPP30	72	142	NumericalError	3.9e-1	1.0e+2	1e-11	81	5.77e+2	13
CERI651ALS	7	0	NumericalError	0	3.8e+1	1e-11	218	3.35e+2	95
CONCON	15	11	NumericalError	7.3e-12	9.0	1e-11	86	-6.23e+3	7
CORE1	65	59	NumericalError	5.0e+4	0	1e-11	85	9.11e+1	33
CRESC50	6	100	RestorationFailed	1.8e-1	1.1e+7	1.2	16	7.86e-1	194
DISCS	36	66	NumericalError	3.9	1.9e+6	6.5e-2	81	1.20e+1	184
ELATTAR	7	102	NumericalError	1e-13	5.7e+15	1e-11	86	7.42e+1	81
FEEDLOC	90	259	NumericalError	1e-8	1.0e+3	6.2e-6	81	-9.54e-10	23
HAHN1LS	7	0	NumericalError	0	1.5	1e-11	87	3.34e+1	78
HAIFAM	99	150	NumericalError	1.7e-11	8.2e+1	1e-11	130	-4.50e+1	40
HS84	5	3	NumericalError	4.4e-3	6.9e+3	5.9e-4	83	-5.28e+6	9
HS99EXP	31	21	NumericalError	1.6e+3	4.2e+10	1.8e-1	84	-1.26e+12	17
HYDC20LS	99	0	NumericalError	0	5.6e-2	1e-11	2307	2.97e-15	639
HYDCAR20	99	99	NumericalError	5.2e-3	0	1e-1	1	0	9
KIRBY2LS	5	0	MaxIterations	0	0	0	144	3.91	11
LAKES	90	78	RestorationFailed	5.5e+2	5.6e+3	8.0e+1	6	3.51e+5	11
LINSPANH	97	33	NumericalError	3e-2	1.0	1e-11	81	-7.70e+1	24
LRCOVTYPE	54	0	Timeout	?	?	?	0	5.72e-1	33
MCONCON	15	11	NumericalError	1.2e-11	9.0	1e-11	92	-6.23e+3	7
MGH10LS	3	0	NumericalError	0	4.7e+11	1e-11	117	8.79e+1	1828
MGH10SLS	3	0	NumericalError	0	1.8e+3	1e-11	81	8.79e+1	354
MSS1	90	73	NumericalError	8.1e-9	4.8	1e-11	81	-1.40e+1	95
MUONSINELS	1	0	NumericalError	0	7.0e-5	1e-11	82	4.39e+4	8
NET1	48	57	NumericalError	1.2e-5	2.1e+2	1.9e-11	123	9.41e+5	26
OET5	5	1002	MaxIterations	4.6e-2	1.0	1e-11	8	2.65e-3	64
OET6	5	1002	NumericalError	1.2e-4	1.6e+9	1e-11	112	2.07e-3	126
OET7	7	1002	NumericalError	2.6e-3	3.0e+19	1e-11	84	4.47e-5	193
PFIT4	3	3	NumericalError	2.5	9.2e-11	3.5e-11	81	0	190
QPCBLEND	83	74	NumericalError	5.3e-1	5.5e+6	1.1e-6	81	-7.84e-3	19
QPNBLEND	83	74	NumericalError	5.3e-1	5.5e+6	1.1e-6	81	-9.14e-3	18
SSINE	3	2	NumericalError	2.4e-2	2.4e-11	1e-11	125	0	224
STRATEC	10	0	NumericalError	0	1.6e+7	3.2e-2	81	2.21e+3	34
SWOPF	83	92	RestorationFailed	9.6e-1	3.9e+12	8.7e-1	66	6.79e-2	13
TAXR13322	72	1261	NumericalError	6.9e-8	1.4e+6	1e-11	110	-3.43e+2	56
THURBERLS	7	0	NumericalError	0	6.5e-4	1e-11	91	5.64e+3	19
TRO3X3	30	13	NumericalError	1.0	3.1e+8	1.1e-4	84	8.97	47
VESUVIOLS	8	0	NumericalError	0	3.0e-4	1e-11	86	9.91e+2	10

Observed Failure Patterns

Pattern 1: mu at floor, large dual infeasibility (24 problems). mu reached 1e-11 but dual infeasibility is still large (1e0 to 1e+15). The barrier subproblem was "solved" but the NLP stationarity conditions are not met. This is the same class of issue as #7 (iterative z corruption), or it indicates that the linear solver produced inaccurate directions that prevented dual convergence. Examples: ELATTAR (du=5.7e+15), MGH10LS (du=4.7e+11), CERI651ALS (du=38), CONCON/MCONCON (du=9.0).

Pattern 2: mu stuck high, primal infeasible (12 problems). mu never decreased below 1e-2, and primal infeasibility is still large. The solver couldn't find a feasible direction from the starting point. Examples: HS99EXP (pr=1.6e+3, mu=0.18), CORE1 (pr=5.0e+4), LAKES (pr=5.5e+2, mu=80). These are globalization failures, likely needing better starting point strategies or more robust restoration.

Pattern 3: Near-converged but stalled (5 problems). Primal is near-feasible and dual is small-ish but just above tolerance. Examples: HAHN1LS (du=1.5), LINSPANH (du=1.0), HYDC20LS (du=0.056), THURBERLS (du=6.5e-4), VESUVIOLS (du=3.0e-4). These might benefit from the z_opt convergence gate fix in v0.6.1 or from tighter iterative refinement.

Pattern 4: Semi-definite data problems (OET5/6/7, TAXR13322). Few variables (5-7) but very many constraints (1002-1261). The KKT system is very rectangular, creating numerical challenges for the augmented system formulation.

Suggested Investigation Priority

1. Near-converged (Pattern 3): Lowest-hanging fruit. May already be fixed by v0.6.1 convergence gate or solvable with minor tolerance/refinement improvements.
2. mu-at-floor dual stall (Pattern 1): Largest group. Root cause is either iterative z corruption (issue Dual infeasibility stalls at ~1e-3 on exp/log objectives #7 class) or linear solver inaccuracy. Better backward error tracking would distinguish these.
3. Globalization failures (Pattern 2): Needs better starting point strategies or restoration improvements.
4. Rectangular problems (Pattern 4): May need the normal equations formulation or iterative solver for the constraint-dominated structure.

[jkitchin]

Status Update (2026-04-11, v0.6.1+)

A lot has changed since this issue was filed. Here is the current state and a root-cause analysis informed by detailed Ipopt and MUMPS source code review.

Progress: 8 of 37 solved, 7 new regressions, net 37 to 36

Solved since filing: ACOPP30*, CONCON, FEEDLOC*, HS99EXP, MCONCON, NET1, TAXR13322*, TRO3X3*
(converges to different local minimum than Ipopt -- valid but different basin)

New ipopt-only regressions: OET4, BATCH, PALMER3, ACOPR30, DECONVBNE, MAKELA3, SPANHYD

Current 36 failures by category

Category	Count	Status breakdown	Root cause
Unconstrained LS/NLS (m=0)	13	11 NumericalError, 1 MaxIter, 1 Timeout	Linear solver accuracy on ill-conditioned J^TJ Hessians
Large constrained (n+m>50)	12	12 NumericalError	KKT system conditioning / mu-at-floor with large dual infeasibility
Rectangular m>>n	6	3 NumericalError, 2 Timeout, 1 RestorationFailed	Dense factorization overhead; condensed KKT conditioning
Small constrained	4	4 NumericalError	Mixed: globalization, multiplier estimation
Globalization	1	1 MaxIterations	Restoration/starting point

Full problem list (36 problems)

Unconstrained LS/NLS (13):
CERI651ALS (n=7), DECONVBNE (n=61), HAHN1LS (n=7), HYDC20LS (n=99), KIRBY2LS (n=5), LRCOVTYPE (n=54), MGH10LS (n=3), MGH10SLS (n=3), MUONSINELS (n=1), PALMER3 (n=4), STRATEC (n=10), THURBERLS (n=7), VESUVIOLS (n=8)

Large constrained (12):
ACOPR30 (72/142), BATCH (46/73), CORE1 (65/59), HAIFAM (99/150), HYDCAR20 (99/99), LAKES (90/78), LINSPANH (97/33), MSS1 (90/73), QPCBLEND (83/74), QPNBLEND (83/74), SPANHYD (97/33), SWOPF (83/92)

Rectangular m>>n (6):
CRESC50 (6/100), ELATTAR (7/102), OET4 (4/502), OET5 (5/1002), OET6 (5/1002), OET7 (7/1002)

Small constrained (4):
HS84 (5/3), MAKELA3 (20/10), PFIT4 (3/3), SSINE (3/2)

Globalization (1):
DISCS (36/66)

Root Cause Analysis

Detailed review of Ipopt source (PDFullSpaceSolver, PDPerturbationHandler, AdaptiveMuUpdate, FilterLSAcceptor) and MUMPS source (dfac_front_aux.F, dfac_driver.F, dsol_driver.F, dini_defaults.F) identified 5 specific mechanisms that Ipopt/MUMPS have but ripopt/rmumps lack:

1. KKT Matrix Scaling (HIGH impact -- affects Classes 1, 2, 3)

• MUMPS applies Ruiz equilibration (KEEP(52)=7) by default for SYM=2. This iteratively scales rows/columns to equilibrate norms: A_scaled = DAD. KKT systems have wildly different scales across blocks; without equilibration, pivot selection degrades because the threshold test compares pivots against unscaled column maxima.
• Ipopt additionally has MC19 scaling (activated on-demand when iterative refinement detects poor quality via IncreaseQuality -> TSymLinearSolver::use_scaling_ = true).
• ripopt/rmumps has no matrix scaling. This alone likely explains many NumericalError failures.

2. Iterative Refinement + Pretend-Singular Fallback (HIGH impact -- Class 1)

• Ipopt does up to 10 rounds of iterative refinement on the full 8-block KKT system (PDFullSpaceSolver.cpp:253-346). Target residual ratio: 1e-10. If refinement fails to reach 1e-5 (residual_ratio_singular), it triggers pretend_singular -> PerturbForSingularity -> increases delta_x -> refactorizes. This chain catches accuracy loss that pivoting alone cannot fix.
• ripopt does 3-5 rounds with no pretend-singular fallback. Poor residuals just log a warning and proceed.

3. Adaptive Mu Safeguards (MEDIUM-HIGH impact -- Class 2)

• Ipopt Free mode checks CheckSufficientProgress() via an obj-constr filter before accepting mu decrease. When progress is insufficient, it switches to Fixed mode with mu = 0.8 * avg_compl, effectively re-raising mu. This prevents mu-at-floor when the NLP is not converging.
• ripopt may be decreasing mu even when dual infeasibility is large, explaining the "mu=1e-11 but du=1e+15" pattern seen in 8+ problems.

4. Structural Degeneracy Detection (MEDIUM impact -- Class 1)

• Ipopt PDPerturbationHandler probes first 3 iterations to detect structurally degenerate Hessians (always need delta_x>0). Once detected, skips the unperturbed factorization attempt, saving wasted work and improving numerical behavior.
• ripopt always tries unperturbed first, wasting iterations on problems where the Hessian is always indefinite.

5. Pivot Tolerance Escalation (MEDIUM impact -- Classes 1, 2)

• Ipopt/MUMPS escalates pivot threshold via pivtol^0.5 (1e-6 -> 1e-3 -> 0.03 -> 0.1) when IncreaseQuality() is called. The aggressive square-root growth reaches maximum quickly.
• ripopt has increase_quality() but the escalation may be less aggressive. The interaction between pivot tolerance and matrix scaling is critical -- scaling first, then lower pivot tolerance works better than high pivot tolerance on unscaled matrices.

Proposed Fix Priority

1. Implement Ruiz equilibration for the KKT matrix before factorization (both dense BK and rmumps paths). This is the single highest-impact change.
2. Add pretend-singular fallback to iterative refinement: if residual ratio > 1e-5 after max rounds, treat as singular and increase delta_x.
3. Add Free-to-Fixed mu re-raise: when switching modes, set mu = 0.8 * avg_compl to prevent premature mu collapse.
4. Structural degeneracy probing for first 3 iterations.
5. Verify condensed KKT activation for OET4/5/6/7 rectangular problems -- these should be O(n^2*m) per iteration, not O(m^3).

[jkitchin]

Progress Update (2026-04-11, commit 4b45311)

All 5 proposed fixes from the earlier analysis have been implemented and merged to main.

Changes Implemented

1. Ruiz equilibration scaling (src/kkt.rs): 3-iteration inf-norm equilibration of the KKT matrix before factorization. Activated on-demand when backward error is poor (matching Ipopt's MC19 on-demand activation and MUMPS's default KEEP(52)=7 for SYM=2).

2. Pretend-singular fallback (src/kkt.rs, src/ipm.rs): Uses Ipopt's normwise residual ratio ||resid||_inf / (min(||sol||_inf, 1e6*||rhs||_inf) + ||rhs||_inf) with threshold 1e-5 (matching residual_ratio_singular). On trigger, tries delta_c first (Jacobian singularity), then delta_w (Hessian singularity), matching Ipopt's PerturbForSingularity path.

3. Adaptive mu dual infeasibility safeguard (src/ipm.rs): Adds du_floor = 0.1 * unscaled_du to compute_barrier_error(), preventing the barrier subproblem from being declared "solved" when NLP dual infeasibility is still large. Also adds du stagnation detection (3-iteration window) that forces Free-to-Fixed mode switch.

4. Structural degeneracy detection (src/kkt.rs): Tracks consecutive iterations needing delta_w > 0. After 3, marks Hessian as structurally degenerate and skips the unperturbed factorization trial (saves one wasted factorization per iteration).

5. Dense BK increase_quality() (src/linear_solver/dense.rs): Configurable Bunch-Kaufman pivot threshold with escalation 0.64 -> 0.8 -> 0.95 -> 1.0 (full pivoting). Previously returned false (no escalation possible).

Additionally: iterative refinement rounds increased from 3-5 to 5-10, and row_abs_max() added to all matrix types for scaling support.

Results on Target Problems

Tested all 35 available issue #8 problems (LRCOVTYPE excluded -- timeout):

Metric	Before	After
Solved	0/35	12/35
NumericalError	30	17
MaxIterations	2	3
Timeout	3	2
RestorationFailed	1	1

Newly solved (objective matches ipopt):

• HYDCAR20, LINSPANH, PFIT4, SSINE, THURBERLS (5 problems, correct objective)

Newly solved (different local minimum):

• ACOPR30, DISCS, HS84, MAKELA3, PALMER3, SPANHYD, SWOPF (7 problems)

Notable improvements among still-failing:

• CERI651ALS: du 38 -> 0.036 (1000x improvement, near convergence)
• HAHN1LS: du 1.5 -> 0.002 (near convergence)
• MGH10LS: NumericalError -> MaxIterations (making progress, needs more iters)

Remaining 23 failures

Category	Count	Problems
NumericalError	17	BATCH, CERI651ALS, CORE1, DECONVBNE, ELATTAR, HAHN1LS, HAIFAM, HYDC20LS, LAKES, MGH10SLS, MSS1, MUONSINELS, OET6, OET7, QPNBLEND, STRATEC, VESUVIOLS
MaxIterations	3	KIRBY2LS, MGH10LS, QPCBLEND
Timeout	2	OET4, OET5
RestorationFailed	1	CRESC50

Next steps for further improvement would focus on MUMPS-specific mechanisms (maximum transversal preprocessing, LDLT-aware ordering) and the near-converged problems (CERI651ALS, HAHN1LS, VESUVIOLS, MUONSINELS) that may need only minor tolerance or refinement tuning.

[jkitchin]

Progress Update (2026-04-11, commit 9ada0bc)

Detailed review of Ipopt source (PDFullSpaceSolver, TSymLinearSolver, AdaptiveMuUpdate) and MUMPS source (dfac_scalings_simScaleAbs.F, dfac_front_aux.F, dini_defaults.F) identified three specific improvements to the linear solve quality chain.

Changes Implemented

1. Ruiz equilibration matches MUMPS SimScale schedule (src/kkt.rs): Changed from 3 inf-norm iterations to 1 inf-norm + 3 one-norm iterations, matching MUMPS KEEP(52)=7 default for SYM=2 (KEEP(231)=1, KEEP(232)=3, KEEP(233)=0). Added row_abs_sum() to all matrix types.

2. IncreaseQuality before perturbation (src/ipm.rs): When PretendSingular triggers (residual ratio > 1e-5 after iterative refinement), now tries IncreaseQuality (Ruiz scaling first, then pivot threshold escalation) BEFORE delta_c/delta_w perturbation. Matches Ipopt PDFullSpaceSolver chain: solve, refine(fail), IncreaseQuality, re-solve, PerturbForSingularity.

3. Iterative refinement improvements (src/kkt.rs): Max refinement steps raised from 5 to 10 for all systems (matching Ipopt max_refinement_steps default). Stagnation detection extended from IC-only to all paths, with relaxed factor (1-1e-6 for non-IC, matching Ipopt residual_improvement_factor = 1-1e-9 spirit).

Key Expert Findings

• Ipopt lower_mu_safeguard is disabled by default (factor=0.0). ripopt du_floor safeguard is non-standard but validated -- 5 previously-solved problems depend on it. Kept as-is.
• MUMPS scaling for SYM=2: SimScale uses SCA(i) /= sqrt(norm_i) per iteration, with 1 inf-norm + 3 one-norm iterations. Previously ripopt used 3 inf-norm iterations.
• Ipopt IncreaseQuality chain: MC19 scaling first (via linear_scaling_on_demand), then MUMPS pivot tolerance escalation (1e-6 -> 1e-3 -> 0.03 -> 0.1 via sqrt). ripopt now mirrors this with Ruiz scaling then BK pivot alpha escalation.
• Always-on scaling for m=0 problems was tested and rejected -- regressed KIRBY2LS and CERI651ALS. On-demand activation is better.

Results

Metric	Before (4b45311)	After (9ada0bc)
Issue 8 solved	12/36	13/36
HS suite	116/120	117/120

Newly solved: KIRBY2LS (n=5, m=0, MaxIterations to Optimal, obj=3.91 matches Ipopt)

Notable improvements among still-failing:

• CERI651ALS: du 595 to 0.00156 (380,000x improvement, obj=335 matches Ipopt, needs about 5 more orders)

No regressions on previously-solved problems.

Remaining 23 failures by category

Category	Count	Root cause
Unconstrained LS (m=0)	10	Linear solve accuracy on ill-conditioned J^TJ Hessians; CERI651ALS is closest to convergence
Large constrained	7	KKT conditioning / sparse solver limitations
Rectangular m>>n	5	Dense factorization overhead; condensed KKT conditioning
Small constrained	1	Globalization

Next steps

The remaining failures are fundamentally limited by linear solver accuracy, not algorithmic gaps. Key directions:

1. Extended precision for small (n<20) unconstrained LS -- compensated summation or double-double in BK factorization
2. MUMPS-style 2x2 pivot identification via maximum transversal matching for large constrained problems
3. Iterative solver fallback (LSMR/MINRES) for rectangular m>>n problems where dense O(m^3) is prohibitive