Dense subset / Core i7-6500U / 2024-07-31 #12
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Free-for-all dense subset
Benchmark reports are copious as we aim to document comparison factors as much as possible. You can also jump to results directly.
Contents
Description
Community-built test set to benchmark QP solvers.
Solvers
All solvers were called via qpsolvers v4.3.2.
CPU info
arch
arch_string_raw
bits
brand_raw
count
cpuinfo_version_string
family
flags
3dnowprefetch
,abm
,acpi
,adx
,aes
,aperfmperf
,apic
,arat
,arch_capabilities
,arch_perfmon
,art
,avx
,avx2
,bmi1
,bmi2
,bts
,clflush
,clflushopt
,cmov
,constant_tsc
,cpuid
,cpuid_fault
,cx16
,cx8
,de
,ds_cpl
,dtes64
,dtherm
,dts
,epb
,ept
,ept_ad
,erms
,est
,f16c
,flexpriority
,flush_l1d
,fma
,fpu
,fsgsbase
,fxsr
,ht
,hwp
,hwp_act_window
,hwp_epp
,hwp_notify
,ibpb
,ibrs
,ida
,intel_pt
,invpcid
,invpcid_single
,lahf_lm
,lm
,mca
,mce
,md_clear
,mmx
,monitor
,movbe
,mpx
,msr
,mtrr
,nonstop_tsc
,nopl
,nx
,osxsave
,pae
,pat
,pbe
,pcid
,pclmulqdq
,pdcm
,pdpe1gb
,pebs
,pge
,pln
,pni
,popcnt
,pse
,pse36
,pti
,pts
,rdrand
,rdrnd
,rdseed
,rdtscp
,rep_good
,sdbg
,sep
,sgx
,smap
,smep
,ss
,ssbd
,sse
,sse2
,sse4_1
,sse4_2
,ssse3
,stibp
,syscall
,tm
,tm2
,tpr_shadow
,tsc
,tsc_adjust
,tsc_deadline_timer
,tscdeadline
,vme
,vmx
,vnmi
,vpid
,x2apic
,xgetbv1
,xsave
,xsavec
,xsaveopt
,xsaves
,xtopology
,xtpr
hz_actual_friendly
hz_advertised_friendly
l1_data_cache_size
l1_instruction_cache_size
l2_cache_associativity
l2_cache_line_size
l2_cache_size
l3_cache_size
model
python_version
stepping
vendor_id_raw
Settings
There are 4 settings: default, high_accuracy, low_accuracy and mid_accuracy. They validate solutions using the following tolerances:
dual
gap
primal
runtime
Solvers for each settings are configured as follows:
tol_feas
tol_gap_abs
tol_gap_rel
feastol
dual_tol
primal_tol
feastol
dual_feasibility_tolerance
primal_feasibility_tolerance
time_limit
tol_comp
tol_eq
tol_ineq
tol_stat
eps_abs
eps_rel
time_limit
check_duality_gap
eps_abs
eps_duality_gap_abs
eps_duality_gap_rel
eps_rel
check_duality_gap
eps_abs
eps_duality_gap_abs
eps_duality_gap_rel
eps_rel
eps_abs
eps_rel
time_limit
predefined_options
time_limit
eps_abs
eps_rel
time_limit_secs
Known limitations
The following issues have been identified as impacting the fairness of this benchmark. Keep them in mind when drawing conclusions from the results.
Results by settings
Default
Solvers are compared over the whole test set by shifted geometric mean (shm). Lower is better, 1.0 is the best.
High accuracy
Solvers are compared over the whole test set by shifted geometric mean (shm). Lower is better, 1.0 is the best.
Low accuracy
Solvers are compared over the whole test set by shifted geometric mean (shm). Lower is better, 1.0 is the best.
Mid accuracy
Solvers are compared over the whole test set by shifted geometric mean (shm). Lower is better, 1.0 is the best.
Results by metric
Success rate
Precentage of problems each solver is able to solve:
Rows are solvers and columns are settings. We consider that a solver successfully solved a problem when (1) it returned with a success status and (2) its solution satisfies optimality conditions within tolerance. The second table below summarizes the frequency at which solvers return success (1) and the corresponding solution did indeed pass tolerance checks.
Percentage of problems where "solved" return codes are correct:
Computation time
We compare solver computation times over the whole test set using the shifted geometric mean. Intuitively, a solver with a shifted-geometric-mean runtime of Y is Y times slower than the best solver over the test set. See Metrics for details.
Shifted geometric mean of solver computation times (1.0 is the best):
Rows are solvers and columns are solver settings. The shift is$sh = 10$ . As in the OSQP and ProxQP benchmarks, we assume a solver's run time is at the time limit when it fails to solve a problem.
Optimality conditions
Primal residual
The primal residual measures the maximum (equality and inequality) constraint violation in the solution returned by a solver. We use the shifted geometric mean to compare solver primal residuals over the whole test set. Intuitively, a solver with a shifted-geometric-mean primal residual of Y is Y times less precise on constraints than the best solver over the test set. See Metrics for details.
Shifted geometric means of primal residuals (1.0 is the best):
Rows are solvers and columns are solver settings. The shift is$sh = 10$ . A solver that fails to find a solution receives a primal residual equal to the full primal tolerance.
Dual residual
The dual residual measures the maximum violation of the dual feasibility condition in the solution returned by a solver. We use the shifted geometric mean to compare solver dual residuals over the whole test set. Intuitively, a solver with a shifted-geometric-mean dual residual of Y is Y times less precise on the dual feasibility condition than the best solver over the test set. See Metrics for details.
Shifted geometric means of dual residuals (1.0 is the best):
Rows are solvers and columns are solver settings. The shift is$sh = 10$ . A solver that fails to find a solution receives a dual residual equal to the full dual tolerance.
Duality gap
The duality gap measures the consistency of the primal and dual solutions returned by a solver. A duality gap close to zero ensures that the complementarity slackness optimality condition is satisfied. We use the shifted geometric mean to compare solver duality gaps over the whole test set. Intuitively, a solver with a shifted-geometric-mean duality gap of Y is Y times less precise on the complementarity slackness condition than the best solver over the test set. See Metrics for details.
Shifted geometric means of duality gaps (1.0 is the best):
Rows are solvers and columns are solver settings. The shift is$sh = 10$ . A solver that fails to find a solution receives a duality gap equal to the full gap tolerance.
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