QP warm-start in first NLP solver iteration #1428
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… more (#1432) ### Added `setup_qp_matrices_and_factorize()`: ``` This function sets up the QP and factorizes Hessian matrix. The current NLP iterate is used to setup the QP iterate, which includes t-slacks. The t and lambda values are clipped according to `solution_sens_qp_t_lam_min` to avoid ill-conditioning. Then the Hessian matrix is factorized. If a two-solver approach is used to obtain solution sensitivities from acados, this function should be called before calling `eval_solution_sensitivity`, or `eval_adjoint_solution_sensitivity()`. This is only implemented for HPIPM QP solver without condensing. ``` ### Key differences of using `setup_qp_matrices_and_factorize()` vs. `solve()` in the two-solver approach: - The QP solver does not need to perform multiple IP iterations to converge and only a single Riccati factorization is performed at the current iterate. - In the chain example this reduces the "Median time to factorize exact Hessian QP:" 450.000 ms to 117.000 ms -> roughly 4x faster 🚀 - In the `solve()`-approach, the Riccati factorization at the second last QP iterate is used, as the system i 6D83 s not factorized at the final QP iterate. However, for the final iterate the system of equations becomes typically ill-conditioned, which is why the final iterate is modified, by clipping the inequality multipliers and t slacks, see option `solution_sens_qp_t_lam_min`. - Less options that have to be set. The options that were needed to use the `solve` approach are now commented: ``` # Old settings needed, when calling solve() instead of setup_qp_matrices_and_factorize() # ocp.solver_options.globalization_fixed_step_length = 0.0 # to not perfrom an SQP step update # ocp.solver_options.nlp_solver_max_iter = 1 # ocp.solver_options.qp_solver_iter_max = 200 # ocp.solver_options.tol = 1e-10 # to "force" a QP solve ``` ### How it works The option `update_fact_exit` was added in HPIPM. This option being active, plus the warm start, plus limiting the QP solver iterations to 0, results in the correct behavior. ### Other things that changed in this PR - fixed warm-starting QP from NLP iterate, was not correctly implemented in #1428, as the QP iterate needs to be condensed and eliminated degrees of freedom need to be taken into account. Only for N==N2 condensing right now, to be extended #1433
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Implement option
nlp_solver_warm_start_first_qp_from_nlp, if True first QP will be initialized using values from NLP iterate, otherwise from previous QP solution, only relevant ifnlp_solver_warm_start_first_qpis True. Default: False.The new initialization (with
nlp_solver_warm_start_first_qp = True) is likely beneficial.We might change the default behavior after more testing.
Fixed option
warm_start_first_qpfor SQP-RTI.