Replace Nonlinear.ReverseAD.Coloring by SparseMatrixColorings

[blegat]

Backport of blegat/ArrayDiff.jl#102

We can now easily use the star coloring 🎉

using JuMP, Ipopt
import MathOptInterface as MOI
import SparseMatrixColorings as SMC

model = Model(Ipopt.Optimizer)
set_silent(model)

# Direct decompression selects star coloring.
algorithm = SMC.GreedyColoringAlgorithm(; decompression = :direct)
set_attribute(
    model,
    MOI.AutomaticDifferentiationBackend(),
    MOI.Nonlinear.SparseReverseMode(algorithm),
)

@variable(model, x, start = -1.2)
@variable(model, y, start = 1.0)
@objective(model, Min, (1 - x)^2 + 100 * (y - x^2)^2)

optimize!(model)

@show termination_status(model)  # LOCALLY_SOLVED
@show value(x) value(y) objective_value(model) # (x, y) ≈ (1, 1), objective ≈ 1.52e-22.

Include workarounds for

• Handle empty symmetric coloring patterns JuliaDiff/SparseMatrixColorings.jl#352
• Support star coloring in decompress_csc! JuliaDiff/SparseMatrixColorings.jl#353

Found performance regressions which should be fixed by:

• Speed up CSC substitution decompression for one-edge trees JuliaDiff/SparseMatrixColorings.jl#354
• Inbounds decompression JuliaDiff/SparseMatrixColorings.jl#355

We should wait for them to be merged and revisit before merging

Closes #2527
Closes #3104

[gdalle]

Any clue how this compares in terms of speed to the existing implementation (acyclic coloring, if memory serves?)?

[mlubin]

Great to see the old code deleted. We need extensive benchmarks before merging.

[blegat]

Raw benchmark results by GPT 6 Astra

The existing implementation uses acyclic coloring. This compares it with the PR’s default SMC acyclic coloring (decompression = :substitution) and optional SMC star coloring (decompression = :direct).

The results are workload-dependent: dense Hessians and larger OPF cases benefit, but the default SMC path is 23–31% slower on the block-dense Hessian evaluations. Star coloring improves those cases, while adding colors and derivative work on chains and grids. The block-dense substitution-recovery regression deserves investigation before merging.

Revisions and environment

• Baseline: 9470528bb94bb0f733167ad8977a31f3391cd155 (the PR parent).
• PR: e29bc6838878eb822c6bea5d3ef349c4ba2c8ab6.
• Julia 1.13.1; SparseMatrixColorings 0.4.28; JuMP 1.32.1; Ipopt 1.16.0; PowerModels 0.21.7; PGLib 0.2.2. Dependencies are identical across the three configurations.
• Linux, Intel Core i7-12700K, pinned to performance CPU 8, one Julia thread and one BLAS thread. Runs were serial.
• 24 synthetic cases (eight families at three sizes), six PGLib AC-OPF cases, and seven complete Ipopt solve cases.

How to read the tables

Phase timings are median (minimum), after warmup. Speedup is baseline median / candidate median: above 1 means faster, below 1 means slower. L / A / S denotes legacy / SMC acyclic / SMC star. Sample counts are shown explicitly; † marks a phase with fewer than five samples in at least one configuration. Those measurements are preliminary.

BenchmarkTools used evals = 1, a 0.4-second budget per phase, and caps of 80 initialization samples or 10,000 Hessian/recovery samples. Timings exclude model construction and compilation. They do not measure time to first solve. These are local measurements on one machine, without statistical confidence intervals.

Evaluator initialization

Fresh evaluator construction and MOI.initialize, including sparsity analysis, coloring, and derivative workspace creation. This is not isolated coloring time.

Case	Legacy (ms)	SMC acyclic (ms)	SMC star (ms)	Acyclic speedup	Star speedup	Samples L / A / S
diagonal_100	0.057 (0.054)	0.082 (0.070)	0.083 (0.067)	0.69×	0.68×	80 / 80 / 80
diagonal_1000	0.762 (0.529)	0.858 (0.681)	0.871 (0.697)	0.89×	0.87×	80 / 80 / 80
diagonal_10000	6.979 (5.601)	8.930 (5.963)	7.804 (6.196)	0.78×	0.89×	50 / 46 / 45
rosenbrock_100	0.144 (0.133)	0.109 (0.101)	0.106 (0.099)	1.32×	1.36×	80 / 80 / 80
rosenbrock_1000	1.448 (1.000)	1.198 (1.055)	1.436 (1.056)	1.21×	1.01×	80 / 80 / 80
rosenbrock_10000	13.243 (11.448)	15.958 (11.091)	16.296 (11.184)	0.83×	0.81×	26 / 26 / 26
bilinear_100	0.038 (0.035)	0.038 (0.037)	0.035 (0.033)	1.00×	1.08×	80 / 80 / 80
bilinear_1000	0.367 (0.314)	0.347 (0.317)	0.327 (0.298)	1.06×	1.12×	80 / 80 / 80
bilinear_10000	3.844 (3.509)	3.760 (3.295)	3.540 (3.197)	1.02×	1.09×	79 / 80 / 80
arrowhead_100	0.078 (0.072)	0.095 (0.091)	0.068 (0.064)	0.82×	1.16×	80 / 80 / 80
arrowhead_1000	2.884 (2.791)	3.430 (3.349)	1.249 (1.212)	0.84×	2.31×	80 / 80 / 80
arrowhead_10000 †	433.203 (433.203)	295.676 (294.249)	76.825 (75.584)	1.47×	5.64×	1 / 2 / 6
grid_10	0.122 (0.114)	0.125 (0.117)	0.118 (0.110)	0.97×	1.03×	80 / 80 / 80
grid_30	1.497 (1.234)	1.475 (1.186)	1.325 (1.058)	1.01×	1.13×	80 / 80 / 80
grid_70	7.996 (7.357)	7.080 (6.666)	6.544 (6.319)	1.13×	1.22×	40 / 46 / 48
blocks_100	0.266 (0.250)	0.181 (0.166)	0.138 (0.126)	1.47×	1.93×	80 / 80 / 80
blocks_1000	2.570 (2.461)	1.813 (1.730)	1.721 (1.358)	1.42×	1.49×	80 / 80 / 80
blocks_5000	16.342 (13.726)	9.758 (9.044)	9.236 (7.348)	1.67×	1.77×	25 / 36 / 44
dense_50	0.586 (0.547)	0.324 (0.311)	0.236 (0.226)	1.81×	2.49×	80 / 80 / 80
dense_150	10.960 (10.416)	5.220 (4.877)	4.099 (3.710)	2.10×	2.67×	34 / 74 / 80
dense_300	77.731 (74.727)	33.399 (31.869)	27.499 (25.163)	2.33×	2.83×	6 / 12 / 15
ocp_20	0.033 (0.032)	0.045 (0.043)	0.042 (0.041)	0.74×	0.79×	80 / 80 / 80
ocp_100	0.167 (0.157)	0.225 (0.211)	0.211 (0.199)	0.74×	0.79×	80 / 80 / 80
ocp_500	0.844 (0.770)	1.189 (1.044)	1.076 (0.979)	0.71×	0.78×	80 / 80 / 80
case14_ieee	0.380 (0.364)	0.361 (0.340)	0.331 (0.315)	1.05×	1.15×	80 / 80 / 80
case118_ieee	4.497 (3.653)	5.409 (3.428)	5.158 (3.246)	0.83×	0.87×	67 / 70 / 72
case300_ieee	12.767 (8.149)	12.009 (7.864)	12.045 (7.859)	1.06×	1.06×	29 / 31 / 32
case1354_pegase	56.191 (45.630)	60.073 (42.433)	60.694 (40.150)	0.94×	0.93×	6 / 7 / 7
case2869_pegase †	169.650 (107.082)	147.454 (102.101)	139.922 (94.707)	1.15×	1.21×	3 / 3 / 3
case10000_goc †	473.387 (361.064)	453.629 (311.030)	413.527 (349.503)	1.04×	1.14×	2 / 2 / 2

Repeated Lagrangian Hessian evaluation

Time per evaluation, obtained from a pair of calls at alternating inputs with nonzero objective and constraint multipliers. Alternation prevents the cached iterate from hiding recomputation. All three configurations reported zero Julia allocations in every case.

Case	Legacy (µs)	SMC acyclic (µs)	SMC star (µs)	Acyclic speedup	Star speedup	Samples L / A / S
diagonal_100	9.34 (8.83)	9.28 (8.85)	9.57 (9.31)	1.01×	0.98×	10,000 / 10,000 / 10,000
diagonal_1000	88.11 (84.09)	89.67 (86.33)	92.40 (89.19)	0.98×	0.95×	2,242 / 2,221 / 2,149
diagonal_10000	926.65 (890.30)	936.35 (903.84)	979.52 (954.97)	0.99×	0.95×	211 / 213 / 201
rosenbrock_100	14.20 (13.58)	14.00 (13.50)	15.09 (14.60)	1.01×	0.94×	10,000 / 10,000 / 10,000
rosenbrock_1000	147.02 (139.82)	145.43 (139.32)	156.71 (149.09)	1.01×	0.94×	1,353 / 1,374 / 1,264
rosenbrock_10000	1,667.47 (1,552.22)	1,573.60 (1,489.56)	1,831.65 (1,740.78)	1.06×	0.91×	117 / 126 / 108
bilinear_100	4.16 (4.04)	4.24 (4.08)	4.36 (4.22)	0.98×	0.96×	10,000 / 10,000 / 10,000
bilinear_1000	39.02 (37.26)	39.69 (38.10)	42.80 (40.53)	0.98×	0.91×	5,110 / 5,011 / 4,560
bilinear_10000	402.76 (383.74)	407.65 (393.66)	436.05 (420.93)	0.99×	0.92×	495 / 489 / 455
arrowhead_100	9.13 (8.78)	9.43 (8.95)	9.23 (8.93)	0.97×	0.99×	10,000 / 10,000 / 10,000
arrowhead_1000	88.39 (85.14)	90.44 (87.32)	89.19 (85.38)	0.98×	0.99×	2,251 / 2,199 / 2,219
arrowhead_10000	904.18 (872.49)	932.49 (902.41)	918.45 (872.86)	0.97×	0.98×	220 / 213 / 217
grid_10	16.95 (16.42)	16.94 (16.48)	18.47 (17.88)	1.00×	0.92×	10,000 / 10,000 / 10,000
grid_30	164.34 (158.91)	166.43 (159.64)	186.72 (176.08)	0.99×	0.88×	1,207 / 1,200 / 1,067
grid_70	980.02 (928.04)	1,004.27 (953.53)	1,116.89 (1,079.29)	0.98×	0.88×	202 / 199 / 179
blocks_100	8.94 (8.63)	10.97 (10.60)	7.38 (7.05)	0.81×	1.21×	10,000 / 10,000 / 10,000
blocks_1000	88.88 (85.51)	116.46 (110.85)	78.75 (74.96)	0.76×	1.13×	2,229 / 1,712 / 2,521
blocks_5000	514.74 (486.57)	660.34 (639.39)	451.81 (410.60)	0.78×	1.14×	387 / 302 / 444
dense_50	13.27 (12.75)	12.74 (12.34)	8.09 (7.68)	1.04×	1.64×	10,000 / 10,000 / 10,000
dense_150	173.30 (165.66)	123.50 (119.56)	79.84 (77.30)	1.40×	2.17×	1,126 / 1,603 / 2,469
dense_300	1,268.50 (1,147.39)	501.15 (481.74)	330.76 (324.24)	2.53×	3.84×	147 / 398 / 598
ocp_20	4.74 (4.54)	4.97 (4.75)	4.81 (4.62)	0.95×	0.98×	10,000 / 10,000 / 10,000
ocp_100	22.70 (21.99)	23.37 (22.52)	22.91 (22.32)	0.97×	0.99×	8,766 / 8,489 / 8,642
ocp_500	127.00 (123.19)	135.75 (130.11)	134.77 (128.43)	0.94×	0.94×	1,556 / 1,458 / 1,464
case14_ieee	40.69 (39.22)	40.68 (38.77)	38.91 (37.46)	1.00×	1.05×	4,860 / 4,873 / 5,058
case118_ieee	480.51 (454.29)	462.91 (441.69)	452.97 (433.53)	1.04×	1.06×	412 / 431 / 434
case300_ieee	2,007.71 (1,387.93)	1,329.83 (1,185.69)	1,290.82 (1,036.76)	1.51×	1.56×	97 / 148 / 147
case1354_pegase	15,386.79 (14,830.75)	13,163.07 (13,032.92)	12,218.16 (11,403.60)	1.17×	1.26×	13 / 16 / 17
case2869_pegase	37,541.92 (36,948.72)	34,495.87 (34,255.83)	30,045.82 (29,399.14)	1.09×	1.25×	6 / 6 / 7
case10000_goc †	108,935.27 (108,909.22)	98,002.50 (97,953.72)	86,786.67 (86,620.97)	1.11×	1.26×	2 / 3 / 3

Isolated Hessian recovery

Recovery of all function Hessians from already compressed products, excluding Hessian-vector products and seed preparation. Every measurement reported zero Julia allocations.

Case	Legacy (µs)	SMC acyclic (µs)	SMC star (µs)	Acyclic speedup	Star speedup	Samples L / A / S
diagonal_100	0.071 (0.068)	0.104 (0.097)	0.173 (0.171)	0.68×	0.41×	10,000 / 10,000 / 10,000
diagonal_1000	0.528 (0.510)	0.818 (0.808)	1.523 (1.484)	0.65×	0.35×	10,000 / 10,000 / 10,000
diagonal_10000	5.058 (4.900)	7.782 (7.571)	14.796 (14.116)	0.65×	0.34×	10,000 / 10,000 / 10,000
rosenbrock_100	0.257 (0.246)	0.389 (0.375)	0.254 (0.250)	0.66×	1.01×	10,000 / 10,000 / 10,000
rosenbrock_1000	2.716 (2.687)	3.724 (3.391)	2.387 (2.375)	0.73×	1.14×	10,000 / 10,000 / 10,000
rosenbrock_10000	28.087 (26.887)	35.289 (34.047)	23.976 (23.240)	0.80×	1.17×	10,000 / 10,000 / 10,000
bilinear_100	0.267 (0.263)	0.294 (0.284)	0.188 (0.176)	0.91×	1.42×	10,000 / 10,000 / 10,000
bilinear_1000	2.667 (2.640)	2.970 (2.825)	1.694 (1.619)	0.90×	1.57×	10,000 / 10,000 / 10,000
bilinear_10000	28.185 (27.550)	28.732 (26.587)	17.009 (15.924)	0.98×	1.66×	10,000 / 10,000 / 10,000
arrowhead_100	0.244 (0.235)	0.386 (0.371)	0.265 (0.260)	0.63×	0.92×	10,000 / 10,000 / 10,000
arrowhead_1000	2.223 (2.183)	3.519 (3.461)	2.345 (2.266)	0.63×	0.95×	10,000 / 10,000 / 10,000
arrowhead_10000	23.250 (22.499)	36.425 (35.150)	23.587 (22.101)	0.64×	0.99×	10,000 / 10,000 / 10,000
grid_10	0.301 (0.288)	0.639 (0.603)	0.419 (0.343)	0.47×	0.72×	10,000 / 10,000 / 10,000
grid_30	3.114 (3.048)	6.391 (6.115)	3.206 (3.117)	0.49×	0.97×	10,000 / 10,000 / 10,000
grid_70	20.238 (19.714)	36.023 (34.373)	16.240 (15.917)	0.56×	1.25×	10,000 / 10,000 / 10,000
blocks_100	2.558 (2.404)	4.697 (4.557)	1.267 (1.159)	0.54×	2.02×	10,000 / 10,000 / 10,000
blocks_1000	17.037 (16.393)	48.197 (46.730)	12.456 (11.332)	0.35×	1.37×	10,000 / 8,194 / 10,000
blocks_5000	98.289 (95.219)	250.601 (241.772)	62.666 (57.055)	0.39×	1.57×	3,995 / 1,581 / 6,387
dense_50	5.867 (5.615)	5.842 (5.714)	1.514 (1.376)	1.00×	3.88×	10,000 / 10,000 / 10,000
dense_150	101.098 (96.388)	55.447 (54.102)	13.408 (12.530)	1.82×	7.54×	3,797 / 7,205 / 10,000
dense_300	907.269 (819.847)	222.109 (215.387)	54.993 (52.363)	4.08×	16.50×	425 / 1,778 / 7,168
ocp_20	0.189 (0.184)	0.212 (0.198)	0.218 (0.210)	0.89×	0.87×	10,000 / 10,000 / 10,000
ocp_100	1.097 (1.081)	1.261 (1.219)	1.200 (1.170)	0.87×	0.91×	10,000 / 10,000 / 10,000
ocp_500	5.418 (5.375)	6.896 (6.236)	5.855 (5.712)	0.79×	0.93×	10,000 / 10,000 / 10,000
case14_ieee	3.616 (3.464)	3.958 (3.828)	1.907 (1.835)	0.91×	1.90×	10,000 / 10,000 / 10,000
case118_ieee	70.630 (68.147)	74.448 (68.136)	34.194 (32.810)	0.95×	2.07×	5,472 / 5,349 / 10,000
case300_ieee	280.595 (194.580)	179.463 (158.502)	89.471 (80.509)	1.56×	3.14×	1,397 / 2,118 / 4,254
case1354_pegase	3,617.634 (3,483.630)	3,367.776 (3,103.445)	1,193.475 (859.913)	1.07×	3.03×	111 / 118 / 337
case2869_pegase	10,251.228 (9,941.418)	8,394.939 (8,185.173)	4,633.145 (4,367.110)	1.22×	2.21×	39 / 48 / 86
case10000_goc	29,232.430 (28,395.734)	24,467.076 (24,160.435)	13,029.897 (12,735.325)	1.19×	2.24×	14 / 17 / 31

Complete Ipopt solves

Each configuration used a fresh model for one warmup solve and three timed solves. Model construction is excluded; derivative initialization during optimize! is included. Times are median [minimum–maximum] in milliseconds. All solves terminated with LOCALLY_SOLVED. Iteration counts were identical across configurations and repetitions.

Case	Legacy (ms)	SMC acyclic (ms)	SMC star (ms)	Acyclic speedup	Star speedup	Iterations
rosenbrock_100	19.754 [19.590–19.867]	19.884 [19.097–20.058]	20.672 [20.209–21.038]	0.99×	0.96×	158
diagonal_1000	4.501 [4.370–4.503]	4.459 [4.422–4.648]	4.446 [4.437–4.816]	1.01×	1.01×	3
grid_30	6.732 [6.614–6.854]	6.472 [6.340–6.699]	6.516 [6.477–6.957]	1.04×	1.03×	5
ocp_100	2.269 [2.179–2.509]	2.347 [2.332–2.409]	2.430 [2.413–2.435]	0.97×	0.93×	4
case14_ieee	7.114 [7.081–7.286]	7.122 [7.072–7.255]	6.964 [6.915–7.120]	1.00×	1.02×	15
case118_ieee	86.707 [81.084–88.261]	78.957 [77.882–79.051]	87.339 [87.166–90.123]	1.10×	0.99×	29
case300_ieee	275.456 [271.873–276.253]	240.009 [237.716–243.478]	259.982 [252.928–266.044]	1.15×	1.06×	33

Solve objectives and Julia allocations

Values below are medians over the three timed solves. Objective values agree to relative/absolute tolerance 1e-6. Allocated bytes cover Julia-managed allocations during optimize!, not native Ipopt allocations or peak memory. MiB = 2²⁰ bytes.

Case	Legacy objective	Acyclic objective	Star objective	Legacy allocated MiB	Acyclic allocated MiB	Star allocated MiB
rosenbrock_100	3.9866238543	3.9866238543	3.9866238543	0.710	0.720	0.737
diagonal_1000	1.64887159137e-21	1.64887159137e-21	1.64887159137e-21	2.652	2.780	2.764
grid_30	3.5865693253e-28	3.5865711647e-28	3.5865711647e-28	5.018	5.093	5.232
ocp_100	24.163216988	24.163216988	24.163216988	0.868	1.084	1.015
case14_ieee	2178.08041082	2178.08041082	2178.08041082	1.773	1.611	1.492
case118_ieee	97213.606939	97213.606939	97213.606939	16.377	14.845	13.743
case300_ieee	565219.971865	565219.971865	565219.971865	36.031	32.618	30.184

Problem dimensions, Hessian structure, and color counts — all 30 cases

n is the number of variables; m counts nonlinear constraints in the evaluator. Hessian entry counts include per-function duplicates. The old implementation adds some structurally zero diagonals that the PR omits. Maximum colors is the largest count over individual objective/constraint functions; total colors and seed entries are summed over those functions. Synthetic grid suffixes are side lengths, and OCP suffixes are horizon lengths.

Case	n	m	Legacy Hessian entries	PR Hessian entries	Max colors L / A / S	Total colors L / A / S	Seed entries L / A / S
diagonal_100	100	0	100	100	1 / 1 / 1	1 / 1 / 1	100 / 100 / 100
diagonal_1000	1,000	0	1,000	1,000	1 / 1 / 1	1 / 1 / 1	1,000 / 1,000 / 1,000
diagonal_10000	10,000	0	10,000	10,000	1 / 1 / 1	1 / 1 / 1	10,000 / 10,000 / 10,000
rosenbrock_100	100	0	199	199	2 / 2 / 3	2 / 2 / 3	200 / 200 / 300
rosenbrock_1000	1,000	0	1,999	1,999	2 / 2 / 3	2 / 2 / 3	2,000 / 2,000 / 3,000
rosenbrock_10000	10,000	0	19,999	19,999	2 / 2 / 3	2 / 2 / 3	20,000 / 20,000 / 30,000
bilinear_100	100	0	199	99	2 / 2 / 3	2 / 2 / 3	200 / 200 / 300
bilinear_1000	1,000	0	1,999	999	2 / 2 / 3	2 / 2 / 3	2,000 / 2,000 / 3,000
bilinear_10000	10,000	0	19,999	9,999	2 / 2 / 3	2 / 2 / 3	20,000 / 20,000 / 30,000
arrowhead_100	100	0	199	198	2 / 2 / 2	2 / 2 / 2	200 / 200 / 200
arrowhead_1000	1,000	0	1,999	1,998	2 / 2 / 2	2 / 2 / 2	2,000 / 2,000 / 2,000
arrowhead_10000	10,000	0	19,999	19,998	2 / 2 / 2	2 / 2 / 2	20,000 / 20,000 / 20,000
grid_10	100	0	280	280	4 / 4 / 5	4 / 4 / 5	400 / 400 / 500
grid_30	900	0	2,640	2,640	4 / 4 / 5	4 / 4 / 5	3,600 / 3,600 / 4,500
grid_70	4,900	0	14,560	14,560	4 / 4 / 5	4 / 4 / 5	19,600 / 19,600 / 24,500
blocks_100	100	0	1,050	1,050	20 / 20 / 20	20 / 20 / 20	2,000 / 2,000 / 2,000
blocks_1000	1,000	0	10,500	10,500	20 / 20 / 20	20 / 20 / 20	20,000 / 20,000 / 20,000
blocks_5000	5,000	0	52,500	52,500	20 / 20 / 20	20 / 20 / 20	100,000 / 100,000 / 100,000
dense_50	50	0	1,275	1,275	50 / 50 / 50	50 / 50 / 50	2,500 / 2,500 / 2,500
dense_150	150	0	11,325	11,325	150 / 150 / 150	150 / 150 / 150	22,500 / 22,500 / 22,500
dense_300	300	0	45,150	45,150	300 / 300 / 300	300 / 300 / 300	90,000 / 90,000 / 90,000
ocp_20	41	22	61	61	1 / 1 / 1	23 / 21 / 21	61 / 61 / 61
ocp_100	201	102	301	301	1 / 1 / 1	103 / 101 / 101	301 / 301 / 301
ocp_500	1,001	502	1,501	1,501	1 / 1 / 1	503 / 501 / 501	1,501 / 1,501 / 1,501
case14_ieee	118	80	800	710	4 / 4 / 4	320 / 320 / 320	1,280 / 1,280 / 1,280
case118_ieee	1,088	744	7,440	6,678	4 / 4 / 4	2,976 / 2,976 / 2,976	11,904 / 11,904 / 11,904
case300_ieee	2,382	1,644	16,440	14,668	4 / 4 / 4	6,576 / 6,576 / 6,576	26,304 / 26,304 / 26,304
case1354_pegase	11,192	7,964	79,640	71,674	4 / 4 / 4	31,856 / 31,856 / 31,856	127,424 / 127,424 / 127,424
case2869_pegase	25,086	18,328	183,280	164,680	4 / 4 / 4	73,312 / 73,312 / 73,312	293,248 / 293,248 / 293,248
case10000_goc	76,804	52,772	527,720	474,948	4 / 4 / 4	211,088 / 211,088 / 211,088	844,352 / 844,352 / 844,352

Initialization allocations and evaluator storage — all 30 cases

Initialization bytes/counts are reported by BenchmarkTools. Evaluator storage is Base.summarysize(evaluator) after initialization and evaluation; it is not peak process memory. MiB = 2²⁰ bytes. Repeated Hessian evaluation and isolated recovery allocate zero bytes in every configuration.

Case	Legacy init MiB	Acyclic init MiB	Star init MiB	Init allocation counts L / A / S	Legacy evaluator MiB	Acyclic evaluator MiB	Star evaluator MiB
diagonal_100	0.265	0.282	0.279	1,872 / 1,987 / 1,951	0.137	0.143	0.142
diagonal_1000	2.607	2.738	2.721	17,210 / 17,338 / 17,300	1.314	1.376	1.360
diagonal_10000	25.476	26.740	26.587	170,227 / 170,359 / 170,321	12.472	13.083	12.930
rosenbrock_100	0.470	0.482	0.499	3,202 / 3,284 / 3,246	0.236	0.246	0.268
rosenbrock_1000	4.475	4.561	4.740	30,259 / 30,339 / 30,289	2.250	2.346	2.567
rosenbrock_10000	45.067	46.007	47.850	300,295 / 300,365 / 300,321	20.083	21.049	23.261
bilinear_100	0.177	0.179	0.179	1,406 / 1,483 / 1,446	0.064	0.068	0.072
bilinear_1000	1.733	1.723	1.727	12,267 / 12,342 / 12,296	0.533	0.568	0.614
bilinear_10000	16.822	16.602	16.690	120,302 / 120,363 / 120,323	5.833	6.188	6.645
arrowhead_100	0.300	0.315	0.305	2,201 / 2,289 / 2,245	0.121	0.131	0.128
arrowhead_1000	2.765	2.883	2.805	20,249 / 20,343 / 20,288	1.151	1.248	1.217
arrowhead_10000	28.103	29.223	28.459	200,277 / 200,369 / 200,314	10.919	11.885	11.579
grid_10	0.559	0.565	0.579	3,447 / 3,440 / 3,397	0.307	0.318	0.340
grid_30	4.948	5.025	5.164	29,573 / 29,526 / 29,476	2.788	2.897	3.105
grid_70	28.441	28.831	29.619	160,914 / 160,832 / 160,782	14.317	14.942	16.088
blocks_100	0.590	0.441	0.358	3,980 / 480 / 432	0.206	0.174	0.151
blocks_1000	3.860	3.799	3.023	5,560 / 1,882 / 1,836	1.467	1.672	1.439
blocks_5000	21.759	22.528	18.519	12,912 / 7,904 / 7,862	7.001	8.319	7.155
dense_50	1.216	0.467	0.357	21,117 / 392 / 344	0.332	0.178	0.149
dense_150	11.507	4.567	3.637	190,404 / 525 / 482	2.815	1.381	1.123
dense_300	46.016	18.113	14.441	763,071 / 723 / 681	11.104	5.318	4.286
ocp_20	0.172	0.218	0.203	2,558 / 3,684 / 3,288	0.078	0.093	0.087
ocp_100	0.820	1.038	0.968	11,710 / 16,997 / 15,161	0.363	0.437	0.407
ocp_500	3.940	5.027	4.682	57,345 / 83,445 / 74,407	1.636	2.021	1.864
case14_ieee	1.663	1.502	1.383	24,787 / 19,969 / 17,871	0.478	0.483	0.445
case118_ieee	15.685	14.165	13.063	230,875 / 185,553 / 166,191	4.452	4.501	4.144
case300_ieee	34.577	31.190	28.756	508,901 / 408,679 / 365,917	9.757	9.859	9.070
case1354_pegase	168.023	151.631	139.842	2,472,911 / 1,987,169 / 1,780,087	46.736	47.315	43.487
case2869_pegase	387.910	345.876	318.748	5,687,432 / 4,569,484 / 4,092,938	107.275	106.899	98.092
case10000_goc	1097.793	991.406	913.297	16,385,836 / 13,166,806 / 11,794,716	299.848	304.979	279.614

Correctness

Assembled Hessians were compared against legacy at two inputs per case, summing duplicate entries and removing structural zeros. All 120 comparisons passed with relative Frobenius-norm error at most 2.61e-15 (tolerance 1e-12). All 90 repeated-Hessian configurations and 90 isolated-recovery configurations reported zero Julia allocations. Solver objectives and iteration counts agree across all seven solve cases; successful local solves do not imply global optimality.

Interpretation

• The default SMC path is close to legacy on many simple sparse cases and faster on dense and several OPF cases, but it is not a uniform speedup.
• The block-dense regression is largely visible in recovery: at 5,000 variables, isolated recovery increases from about 98 to 251 µs, while the whole Hessian evaluation increases from 515 to 660 µs, with identical color counts and seed sizes.
• Star coloring is a tradeoff: on Rosenbrock chains it uses three colors instead of two, and on grids five instead of four. Cheaper recovery does not always offset the extra derivative work.
• Setup costs also matter: default SMC initialization is 35–41% slower on the optimal-control examples, while dense cases benefit substantially.
• These chosen cases do not represent the distribution of all MOI workloads. Longer sampling is needed for the marked largest cases before making precise performance claims.

[blegat]

I made PR to SMC to address the performance regressions, see update PR description