@@ -27,7 +27,7 @@ subject to
2727plus boundary, control and state constraints
2828
2929- Our core interests: numerical & geometrical methods in control, applications
30- - Why Julia: fast (+ JIT), strongly typed, high-level (AD, macros), available fast optimisation and ODE solvers, rapidly growing community
30+ - Why Julia: fast (+ JIT), strongly typed, high-level (AD, macros), fast optimisation and ODE solvers available , rapidly growing community
3131
3232``` @raw html
3333<img width="800" alt="juliacon2025" src="./assets/juliacon2025.jpg">
@@ -54,7 +54,7 @@ b(t_0, X_0, t_N, X_N) = 0
5454```
5555
5656``` math
57- g(t_i, X_i, U_i) = 0,\quad i = 0,\dots,N
57+ g(X_i, U_i) = 0,\quad i = 0,\dots,N
5858```
5959
6060- SIMD parallelism ($f0$, $f$, $g$) + sparsity: Kernels for GPU ([ KernelAbstraction.jl] ( https://juliagpu.github.io/KernelAbstractions.jl/stable/ ) ) and sparse linear algebra ([ CUDSS.jl] ( https://github.com/exanauts/CUDSS.jl ) )
293293``` @raw html
294294</details>
295295```
296-
297- - ** Remark.** Automated scalarisation of (linear) range constraints
298- ``` julia
299- XXXX
300- ```
301296- Solving (MadNLP + CUDSS)
302297``` julia
303298This is MadNLP version v0.8.7 , running with cuDSS v0.4.0
@@ -319,27 +314,27 @@ iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
319314 0 1.0000000e-01 1.10e+00 1.00e+00 - 1.0 0.00e+00 - 0.00e+00 0.00e+00 0
320315 1 1.0001760e-01 1.10e+00 3.84e-03 - 1.0 6.88e+02 - 4.0 1.00e+00 2.00e-07 h 2
321316 2 - 5.2365072e-03 1.89e-02 1.79e-07 - 1.0 6.16e+00 - 4.5 1.00e+00 1.00e+00 h 1
322- 3 5.9939627e +00 2.28e-03 1.66e-04 - 3.8 6.00e+00 - 5.0 9.99e-01 1.00e+00 h 1
323- 4 5.9996194e +00 3.00e -06 1.05e-06 - 3.8 7.77e -02 - 1.00e+00 1.00e+00 h 1
317+ 3 5.9939621e +00 2.28e-03 1.66e-04 - 3.8 6.00e+00 - 5.0 9.99e-01 1.00e+00 h 1
318+ 4 5.9996210e +00 2.94e -06 8.38e-07 - 3.8 7.70e -02 - 1.00e+00 1.00e+00 h 1
324319
325320Number of Iterations.... : 4
326321
327322 (scaled) (unscaled)
328- Objective............... : 5.9996194116826898e +00 5.9996194116826898e +00
329- Dual infeasibility...... : 1.0504883830561350e-06 1.0504883830561350e-06
330- Constraint violation.... : 2.9972943093481582e -06 2.9972943093481582e -06
331- Complementarity......... : 2.0007458990898193e -06 2.0007458990898193e -06
332- Overall NLP error....... : 2.9972943093481582e -06 2.9972943093481582e -06
323+ Objective............... : 5.9996210189633494e +00 5.9996210189633494e +00
324+ Dual infeasibility...... : 8.3756005011360529e-07 8.3756005011360529e-07
325+ Constraint violation.... : 2.9426923277963834e -06 2.9426923277963834e -06
326+ Complementarity......... : 2.0007459547789288e -06 2.0007459547789288e -06
327+ Overall NLP error....... : 2.9426923277963834e -06 2.9426923277963834e -06
333328
334329Number of objective function evaluations = 6
335330Number of objective gradient evaluations = 5
336331Number of constraint evaluations = 6
337332Number of constraint Jacobian evaluations = 5
338333Number of Lagrangian Hessian evaluations = 4
339- Total wall- clock secs in solver (w/ o fun. eval./ lin. alg.) = 0.423
340- Total wall- clock secs in linear solver = 0.055
341- Total wall- clock secs in NLP function evaluations = 0.005
342- Total wall- clock secs = 0.483
334+ Total wall- clock secs in solver (w/ o fun. eval./ lin. alg.) = 0.072
335+ Total wall- clock secs in linear solver = 0.008
336+ Total wall- clock secs in NLP function evaluations = 0.003
337+ Total wall- clock secs = 0.083
343338```
344339- [ Goddard problem] ( https://control-toolbox.org/Tutorials.jl/stable/tutorial-goddard/ )
345340``` julia
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