Benchmarks

This page reports numerical results on an NVIDIA A100-SXM4-80GB GPU.

Numerical Results

  • HPR-QP is implemented in Julia and leverages CUDA for GPU acceleration.

  • PDQP (GPU, downloaded in April 2025).

  • SCS (GPU, v2.1.0)is written in C/C++ with a Julia interface. GPU acceleration is enabled via its indirect solver, which performs all matrix operations on the GPU.

  • CuClarabel (GPU, v0.10.0).

  • Gurobi (CPU, version 12.0.2, academic license) is executed on CPU using the barrier method.

  • All benchmarks were conducted on a SuperServer SYS-420GP-TNR with an NVIDIA A100-SXM4-80GB GPU, Intel Xeon Platinum 8338C CPU @ 2.60 GHz, and 256 GB RAM

Maros–Mészáros Data Set (137 Instances; tolerances \(10^{-6}\) and \(10^{-8}\))

Solver

SGM10 (1e-6)

Solved (1e-6)

SGM10 (1e-8)

Solved (1e-8)

HPR-QP

10.5

129

12.6

128

PDQP

33.1

125

42.5

124

SCS

126.0

103

165.0

93

CuClarabel

3.7

130

7.8

124

Gurobi

0.4

137

1.2

135

QAP Relaxations (36 Instances; tolerances \(10^{-6}\) and \(10^{-8}\))

Solver

SGM10 (1e-6)

Solved (1e-6)

SGM10 (1e-8)

Solved (1e-8)

HPR-QP

1.8

36

4.7

36

PDQP

124.1

23

149.4

23

SCS

11.3

36

86.0

36

CuClarabel

13.6

33

114.9

22

Gurobi

24.8

36

26.8

36

LASSO Problems (11 Instances; tolerance \(10^{-8}\))

Abbreviations: T = time-limit, F = failure (e.g., unbounded or infeasible).

Instance

HPR-QP

PDQP

SCS

CuClarabel

Gurobi

abalone7

10.5

372.5

T

24.4

127.3

bodyfat7

1.2

33.3

T

2.2

30.8

E2006.test

0.2

1.3

T

15.4

9.0

E2006.train

0.7

1.9

F

116.0

277.8

housing7

22.6

123.3

T

5.7

125.9

log1p.E2006.test

7.0

1416.9

T

196.0

137.0

log1p.E2006.train

17.3

2983.2

T

361.0

878.8

mpg7

0.6

18.1

2000.0

0.3

1.2

pyrim5

49.1

410.6

T

3.5

35.9

space_ga9

0.6

62.7

1210.0

6.7

38.1

triazines4

401.3

3533.3

T

26.0

843.1

SGM10 (time)

13.2

161.8

3091.0

26.1

91.2