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NLPModels

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This package provides general guidelines to represent optimization problems in Julia and a standardized API to evaluate the functions and their derivatives. The main objective is to be able to rely on that API when designing optimization solvers in Julia.

How to Cite

If you use NLPModels.jl in your work, please cite using the format given in CITATION.bib.

Optimization Problems

Optimization problems are represented by an instance of (a subtype of) AbstractNLPModel. Such instances are composed of

• an instance of NLPModelMeta, which provides information about the problem, including the number of variables, constraints, bounds on the variables, etc.
• other data specific to the provenance of the problem.

See the documentation for details on the models and the API.

Installation

pkg> add NLPModels

Models

This package provides no models, although it allows the definition of manually written models.

Check the list of packages that define models in this page of the docs

Main Methods

If model is an instance of an appropriate subtype of AbstractNLPModel, the following methods are normally defined:

• obj(model, x): evaluate f(x), the objective at x
• cons(model x): evaluate c(x), the vector of general constraints at x

The following methods are defined if first-order derivatives are available:

• grad(model, x): evaluate ∇f(x), the objective gradient at x
• jac(model, x): evaluate J(x), the Jacobian of c at x as a sparse matrix

If Jacobian-vector products can be computed more efficiently than by evaluating the Jacobian explicitly, the following methods may be implemented:

• jprod(model, x, v): evaluate the result of the matrix-vector product J(x)⋅v
• jtprod(model, x, u): evaluate the result of the matrix-vector product J(x)ᵀ⋅u

The following method is defined if second-order derivatives are available:

• hess(model, x, y): evaluate ∇²L(x,y), the Hessian of the Lagrangian at x and y

If Hessian-vector products can be computed more efficiently than by evaluating the Hessian explicitly, the following method may be implemented:

• hprod(model, x, v, y): evaluate the result of the matrix-vector product ∇²L(x,y)⋅v

Several in-place variants of the methods above may also be implemented.

The complete list of methods that an interface may implement can be found in the documentation.

Attributes

NLPModelMeta objects have the following attributes (with S <: AbstractVector):