Manual sparsity patterns for generic IRK with stagewise controls

[PierreMartinon]

Note: the changes from the stepwise constant control version are rather straightforward since the main difference is the size of the control variables block for each step (s instead of just 1).

Similarly to previous experiments, using manual sparsity patterns becomes faster for larger grid sizes, for instance starting around 1000 time steps for the benchmark below on a set of easy problems.

Keep in mind that the manual sparsity patterns could be significantly improved by computing the patterns for each OCP function and use them to build the Jacobian/Hessian patterns, instead of assuming full dense derivatives as in the current version.

julia> bench(; scheme=:gauss_legendre_2, timer=true, grid_size_list=[250,500,1000,2000])
Problem list: ["beam", "double_integrator_mintf", "double_integrator_minenergy", "electric_vehicle", "fuller", "goddard", "goddard_all", "jackson", "simple_integrator", "vanderpol"]
Grid size list: [250, 500, 1000, 2000]
beam                       0.11( 20)   0.26( 22)   0.69( 29)   1.72( 29) 
double_integrator_tf       0.12( 16)   0.34( 21)   1.05( 19)   3.18( 17) 
double_integrator_e        0.03(  1)   0.07(  1)   0.17(  1)   0.61(  1) 
electric_vehicle           0.15(  6)   0.40(  6)   1.58(  6)   5.56(  6) 
fuller                     0.13( 15)   0.23( 12)   0.52( 10)   1.26(  9) 
goddard                    1.48( 36)   3.90( 39)  11.66( 39)  27.02( 42) 
goddard_all_constraints    0.90( 21)   3.18( 23)   6.97( 23)  24.03( 24) 
jackson                    0.43( 29)   1.11( 27)   3.53( 34)  11.09( 22) 
simple_integrator          0.06(  8)   0.13(  8)   0.33(  8)   1.02(  8) 
vanderpol                  0.13(  3)   0.38(  3)   1.40(  3)   5.60(  3) 

SUCCESS 40/40      3.55(155)  10.00(162)  27.91(172)  81.10(161) 

julia> bench(; scheme=:gauss_legendre_2, timer=true, grid_size_list=[250,500,1000,2000], adnlp_backend=:manual)
Problem list: ["beam", "double_integrator_mintf", "double_integrator_minenergy", "electric_vehicle", "fuller", "goddard", "goddard_all", "jackson", "simple_integrator", "vanderpol"]
Grid size list: [250, 500, 1000, 2000]
beam                       0.26( 20)   0.69( 21)   2.22( 30)   5.10( 33) 
double_integrator_tf       0.20( 16)   0.71( 21)   1.39( 19)   2.90( 17) 
double_integrator_e        0.04(  1)   0.08(  1)   0.17(  1)   0.37(  1) 
electric_vehicle           0.16(  6)   0.34(  6)   0.73(  6)   1.62(  6) 
fuller                     0.22( 15)   0.42( 12)   0.76( 10)   1.62(  9) 
goddard                    1.48( 36)   4.61( 39)   8.96( 39)  16.54( 38) 
goddard_all_constraints    0.82( 21)   2.04( 23)   3.36( 15)  12.57( 26) 
jackson                    0.80( 29)   1.71( 27)   4.51( 34)   6.69( 22) 
simple_integrator          0.09(  8)   0.19(  8)   0.43(  8)   0.89(  8) 
vanderpol                  0.09(  3)   0.20(  3)   0.41(  3)   0.87(  3) 

SUCCESS 40/40      4.16(155)  10.98(161)  22.94(165)  49.17(163) 

[github-actions]

Breakage test results
Date: 2026-05-04 12:16:31

Name	Latest	Stable
OptimalControl	compat: v1.0.11	compat: v1.0.11