NLPModels.jl documentation

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.

Current NLPModels.jl works on Julia 1.0.

Introduction

The general form of the optimization problem is

where $f:\mathbb{R}^n\rightarrow\mathbb{R}$, $c:\mathbb{R}^n\rightarrow\mathbb{R}^m$, $E\cup I = \{1,2,\dots,m\}$, $E\cap I = \emptyset$, and $c_{L_i}, c_{U_i}, \ell_j, u_j \in \mathbb{R}\cup\{\pm\infty\}$ for $i = 1,\dots,m$ and $j = 1,\dots,n$.

For computational reasons, we write

defining $c_{L_i} = c_{U_i}$ for all $i \in E$. The Lagrangian of this problem is defined as

where $\sigma$ is a scaling parameter included for computational reasons. Notice that, for the Hessian, the variables $z^L$ and $z^U$ are not used.

Optimization problems are represented by an instance/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.

Nonlinear Least Squares

A special type of NLPModels are the NLSModels, i.e., Nonlinear Least Squares models. In these problems, the function $f(x)$ is given by $\tfrac{1}{2}\Vert F(x)\Vert^2$, where $F$ is referred as the residual function. The individual value of $F$, as well as of its derivatives, is also available.

Tools

There are a few tools to use on NLPModels, for instance to query whether the problem is constrained or not, and to get the number of function evaluations. See Tools.

Install

Install NLPModels.jl with the following command.

pkg> add NLPModels

This will enable a simple model and a model with automatic differentiation using ForwardDiff. For models using JuMP see NLPModelsJuMP.jl.

Usage

See the Models, the Tools, the Tutorial, or the API.

Internal Interfaces

• ADNLPModel: Uses ForwardDiff to compute the derivatives. It has a very simple interface, though it isn't very efficient for larger problems.
• SimpleNLPModel: Only uses user defined functions.
• SlackModel: Creates an equality constrained problem with bounds on the variables using an existing NLPModel.
• LBFGSModel: Creates a model using a LBFGS approximation to the Hessian using an existing NLPModel.
• LSR1Model: Creates a model using a LSR1 approximation to the Hessian using an existing NLPModel.
• ADNLSModel: Similar to ADNLPModel, but for nonlinear least squares.
• FeasibilityResidual: Creates a nonlinear least squares model from an equality constrained problem in which the residual function is the constraints function.
• LLSModel: Creates a linear least squares model.
• SimpleNLSModel: Similar to SimpleNLPModel, but for nonlinear least squares.
• SlackNLSModel: Creates an equality constrained nonlinear least squares problem with bounds on the variables using an existing NLSModel.
• FeasibilityFormNLS: Creates residual variables and constraints, so that the residual is linear.

External Interfaces

• AmplModel: Defined in AmplNLReader.jl for problems modeled using AMPL
• CUTEstModel: Defined in CUTEst.jl for problems from CUTEst.
• MathProgNLPModel: Uses a MathProgModel, derived from a AbstractMathProgModel model. For instance, JuMP.jl models can be used.

If you want your interface here, open a PR.

Attributes

NLPModelMeta objects have the following attributes:

License

This content is released under the MPL2.0 License.

Contents

• API
• Reference guide
• API for NLSModels
• AbstractNLPModel functions
• AbstractNLSModel
• Derivative Checker
• Internal
• Models
• ADNLPModel
• SimpleNLPModel
• Derived Models
• ADNLSModel
• FeasibilityResidual
• LLSModel
• SimpleNLSModel
• SlackNLSModel
• FeasibilityFormNLS
• Reference
• NLPModels.jl documentation
• Introduction
• Nonlinear Least Squares
• Tools
• Install
• Usage
• Internal Interfaces
• External Interfaces
• Attributes
• License
• Contents
• Tools
• Functions evaluations
• Querying problem type
• Docs
• Tutorial
• ADNLPModel Tutorial
• SimpleNLPModel Tutorial
• Nonlinear least squares models