This PR implements a new globalization method that is based on a funnel.
It can be used by setting the option `globalization` to
`FUNNEL_L1PEN_LINESEARCH` and is detailed below.
In addition, the PR contains the following general new options:
- `eval_residual_at_max_iter`: boolean that decides if the residuals
(and function and derivatives) will be evaluated in the last iteration.
The previous behavior of the SQP method is to _not_ evaluate again at
max iter. For the funnel methode, the default is true.
- `nlp_solver_tol_min_step_norm`: If this option is set to a value
larger than zero, the solver will terminate if a step size smaller than
the given value is encountered.

## Funnel method
A funnel method can be seen as a simplification of a filter method that
can achieve similar performance in terms of robustness. The implemented
algorithm uses a line search for step size determination. Additionally,
a penalty phase is implemented that should handle infeasible subproblems
similiarly to a feasibility restoration as, e.g., implemented in IPOPT.
The work on the funnel is subject of current research. Therefore, we are
currently working on an article that describes the algorithm in detail.

This PR includes the following features:
- new globalization strategy based on a funnel: The funnel is an upper
bound on constraint violation, that drives globalization. In case no
progress can be made, a penalty phase is incorporated that avoids a
feasibility restoration phase.
- an improvement of the termination criterion. Unbounded problems can be
detected, as well as when the algorithm converges to suboptimal point
and the step size goes below a given threshold.
- The iteration output for the `FUNNEL_L1PEN_LINESEARCH` includes more
data about the globalization parameters.
- The current `FUNNEL_L1PEN_LINESEARCH` globalization is tested on
feasibility problems and on some simple OCPs.

The following new funnel related options are added:
- `funnel_initialization_increase_factor`: initialization of funnel
width: `max(funnel_initialization_upper_bound,
funnel_initialization_increase_factor * initial_infeasibility)`
- `funnel_initialization_upper_bound`: see line above
- `funnel_sufficient_decrease_factor`: h-type steps need to declare
sufficient decrease in constraint violation wrt funnel
- `funnel_kappa`: convex combination factor for funnel decrease function
- `funnel_fraction_switching_condition`: fraction in switching condition
used for distinguishing between f and h steps
- `funnel_initial_penalty_parameter`: initialization of penalty
parameter, used in penalty phase that replaces a feasibility
restoration. This penalty parameter will later be used in l1 relaxation.

Disclaimer: The current funnel implementation is still preliminary. For
example, infeasible QPs cannot be handled yet which can mitigate the
convergence behavior of certain problems.

---------

Co-authored-by: Jonathan Frey <[email protected]>
Co-authored-by: sandmaennchen <[email protected]>

This PR is a first step towards aligning the MATLAB interface with the
python interface.

python changes:

- new attributes `dyn_impl_dae_fun_jac`, `dyn_impl_dae_jac`,
`dyn_impl_dae_fun` in the `AcadosModel` for generic external implicit
dynamics
- new attribute `nlp_solver_warm_start_first_qp` in `AcadosOptions`

MATLAB changes:
- Renaming of internal classes `acados_<...>_json` to match
corresponding python class `Acados...`
- lots of option defaults added which are already available in python
- remove `rti_phase` in formulation object, as it only makes sense to
change this online

…ve unused memory, add tests (#1162)

- fix: `external_function_param_casadi` class for the case when the
parameters are not a dense vector. This is still not recommended
- removed unused memory requirement of `np` in
`external_function_param_casadi`.
- added static functions `d_cvt_ext_fun_arg_to_casadi`,
`d_cvt_casadi_to_ext_fun_arg` to avoid code duplication

Tests:
- added `examples/acados_python/tests/sparse_param_test.py`
- improved test of parametric OCP formulation

---------

Co-authored-by: sandmaennchen <[email protected]>

Previously parameter values could be set function wise and stage wise.

- add external function classes:
`external_function_external_param_casadi`,
`external_function_external_param_generic`. These classes contain a
pointer to the parameter values instead of a memory.
- Adjust OCP solver templates (single- and multi-phase) to use the new
classes.
- Parameter vectors are now only stored once per stage in `ocp_nlp_in`

This allows to update parameters faster and lowers memory footprint.
Moreover, it will be possible to get parameter values which allows to
perform tests on parameters and more.

- Integrator not changes (yet). Benefit is that
`external_function_param_casadi` is still tested.

This PR adds Nan and Inf detection in merit function based line search.
If Nan/inf is encountered during the evaluation of the merit function,
the step size is decreased. If Nan/inf is encountered during the early
termination check, no second-order corrections are performed.

Follow-up: backtrack if new linearization results in NaN or infeasible
QP.

- split into functions
- separate function for preliminary line search before SOC
- reset merit function weights when doing SOC. This is the only change
affecting the behavior of the algorithm in this PR.
- adjusted test to account for point above.

- use `OSQP_INFITY`
- comments on how to export QP for Gianluca
- improve example

…dosSim` (#1170)

This PR changes the code generation of CasADi functions in MATLAB such
that it is solely based on the OCP description used of the template
interface, i.e. `AcadosOcp`. Similar for integrators where only
`AcadosSim` is used for code generation.

Progress maximization example in 3D using the Frenet-Serret Formulas.

Dimensions: nx : 20, nu : 4, nh : 1, N : 50
Solver : HPIPM
Integrator : Explicit RK4

---------

Co-authored-by: akash <[email protected]>

- SQP & DDP: move regularize before check_termination, such that we can
get the QP at the stationary point that is actually solved, if we exit
with success.
- MEX: add functions `dump_last_qp_to_json`, `qp_diagnostics`

---------

Co-authored-by: sandmaennchen <[email protected]>

- added functionality in Matlab interface:
`ocp_solver.set_params_sparse(idx_values, new_p_values, stage);`. This
updates the parameters with indices `idx_values` (0 based) at `stage`
with the new values `new_p_values`.
- Added getters for parameter values `p` in Matlab and Python.
- Tests for parameter setters are added, both in Matlab and Python.

…mpiler (#1178)

- empty array does not work with some compilers
- nothing has to be set if parameter vector is empty, thus added if in
template
- reported in
https://discourse.acados.org/t/minimal-example-ocp-m-error/1702
- introduced in #1176

Dependabot was sending mails about known security vulnerabilities
detected in the dependency Jinja2 Version < 3.1.4

- Simulink: add possible output `parameter_traj`, for testing
- test setting and getting parameters in Simulink in
`simulink_param_test`
- add function `add_sparse_param_port_simulink(simulink_opts, idx_p,
port_name, stage_idx_0, stage_idx_e)` in Matlab, which allows to specify
information for an input port of the simulink block corresponding to an
acados OCP solver. Inputs are
- `idx_p` is a 0-based vector of parameter indices to be updated by the
port.
    - `port_name` is used to identify the port and print information.
- `stage_idx_0` is the first stage for which the parameters should be
updated by the port (in `[0, N]`).
- `stage_idx_e` is the last stage for which the parameters should be
updated by the port (in `[stage_idx_0, N]`).

- The resulting port gets as inputs:
- first one: value which indicates if update should be performed (0
means no update).
- afterwards: new numerical values of parameters to be updated at stages
specified by `stage_idx_0`, `stage_idx_e`.
- size of input port: 1 + (`stage_idx_e` - `stage_idx_0` + 1) *
length(`idx_p`)

- test sparse parameter update ports in Simulink

- update HPIPM with latest fix
giaf/hpipm@3ab7d60
- set HPIPM mode to ROBUST in example which did not work before HPIPM
upgrade, see
33730ae

…1180)

Following up on the acados logo design contest
https://discourse.acados.org/t/logo-design-contest/1502/6

---------

Co-authored-by: sandmaennchen <[email protected]>

OSQP moved to a dedicated organization a while ago, so this updates all
the docs references and the submodule to point to the new organization.