# Guidelines for creating models

These are guidelines for the creation of models using NLPModels to help keeping the models uniform, and for future reference in the creation of solvers.

## Bare minimum

Your model should derive from AbstractNLPModel or some other abstract class derived from it. It is mandatory that it have a meta :: NLPModelMeta field, storing all the relevant problem information. The model also needs to provide Counters information. The easiest way is to define counters :: Counters. For instance:

mutable struct MyModel{T, S} <: AbstractNLPModel{T, S}
meta :: NLPModelMeta{T, S}
counters :: Counters
end

For alternatives to storing Counters in the model, check advanced counters. The minimum information that should be set for your model through NLPModelMeta is nvar, the number of variables. The following is a valid constructor for MyModel:

function MyModel()
return MyModel(NLPModelMeta(5), Counters())
end

More information can be passed to NLPModelMeta. See the full list here. The essential fields are

• x0: Starting point (defaults to zeros)
• lvar, uvar: Bounds on the variables (default to (-∞,∞))
• ncon: Number of constraints (defaults to 0)
• lcon, ucon: Bounds on the constraints (default to (-∞,∞))
• nnzh: The length of the vectors used to store a triangle of the Hessian in triplet format (defaults to nvar * (nvar + 1) / 2
• nnzj: The length of the vectors used to store the Jacobian in triplet format (default to nvar * ncon)

There are about 30 functions in the NLPModels API, and a few with more than one signature. Luckily, many have a default implementation. We collect here the list of functions that should be implemented for a complete API.

Here, the following notation apply:

• nlp is your instance of MyModel <: AbstractNLPModel
• x is the point where the function is evaluated
• y is the vector of Lagrange multipliers (for constrained problems only)
• g is the gradient vector
• H is the Hessian of the objective or Lagrangian
• hrows, hcols, and hvals are vectors storing the triplet form of the Hessian
• c is the vector of constraints
• J is the Jacobian of the constraints
• jrows, jcols, and jvals are vectors storing the triplet form of the Jacobian
• v is a vector of appropriate dimensions, generally used for operator-vector products
• Jv, Jtv, Hv are vectors of appropriate dimensions, storing the result of operator-vector products

The following functions should be defined:

• Objective (unconstrained models only need to worry about these)
• obj(nlp, x)
• grad!(nlp, x, g)
• hess_structure!(nlp, hrows, hcols)
• hess_coord!(nlp, x, hvals; obj_weight=1)
• hprod!(nlp, x, v, Hv; obj_weight=1) (actually defaults to calling the constrained case)
• Constraints (constrained models need to worry about these and the ones above)
• cons_lin!(nlp, x, c)
• cons_nln!(nlp, x, c)
• jac_lin_structure!(nlp, jrows, jcols)
• jac_nln_structure!(nlp, jrows, jcols)
• jac_lin_coord!(nlp, x, jvals)
• jac_nln_coord!(nlp, x, jvals)
• jprod_lin!(nlp, x, v, Jv)
• jprod_nln!(nlp, x, v, Jv)
• jtprod_lin!(nlp, x, v, Jtv)
• jtprod_nln!(nlp, x, v, Jtv)
• hess_coord!(nlp, x, y, hvals; obj_weight=1)
• hprod!(nlp, x, y, v, Hv; obj_weight=1)

The linear constraints are specified at the initialization of the NLPModelMeta using the keyword arguement lin. The indices of linear and nonlinear constraints are respectively available in nlp.meta.lin and nlp.meta.nln. If your model uses only linear (resp. nonlinear) constraints, then it suffices to implement the *_lin (resp. *_nln) functions. Alternatively, one could implement only the functions without the suffixes _nln! (e.g., only cons!), but this might run into errors with tools differentiating linear and nonlinear constraints.

## Expected behaviour

The following is a non-exhaustive list of expected behaviour for methods.

• All in place methods should also return the modified vectors.
• Vector inputs should have the correct size. If necessary, the user should pass them using views or slices.
• The triplet format does not assume order nor uniqueness.

## Show

To further specialize your model, you can also define show_header and possibly show. The default show_header simply prints the typeof the NLPModel, so it should be specialized with the specific information that you prefer. For instance, SlackModel defines

show_header(io :: IO, nlp :: SlackModel) = println(io, "SlackModel - Model with slack variables")

Furthermore, we define a general show that calls show_header and specific show functions for the meta and the counters. If your model does not have counters in the default location, you must define show for them as well. Alternatively, you may desire to change the behaviour of show. Here is an example, again from SlackModel:

function show(io :: IO, nlp :: SlackModel)
show(io, nlp.meta)
show(io, nlp.model.counters)
end

If a model does not implement counters, then it needs to define

• neval_xxx(nlp) - get field xxx of Counters
• reset!(nlp) - resetting all counters
• increment!(nlp, s) - increment counter s

For instance

for counter in fieldnames(Counters)
@eval begin
$counter(nlp :: MyModel) = SOMETHING end end function reset!(nlp :: MyModel) RESET COUNTERS end function increment!(nlp :: MyModel, s :: Symbol) INCREMENT COUNTER s end One example of such model is the SlackModel, which stores an internal model :: AbstractNLPModel, thus defining $counter(nlp :: SlackModel) = \$counter(nlp.model)
reset!(nlp :: SlackModel) = reset!(nlp.model)
increment!(nlp :: SlackModel, s :: Symbol) = increment!(nlp.model, s)

This construction can be replicated calling the macro @default_counters Model inner. In the case of SlackModel, the equivalent call is

@default_counters SlackModel model

Furthermore, the show method has to be updated with the correct direction of counter. See show for more information.