nsajko / tulip.jl

Interior-point solver in pure Julia

Tulip

Documentation	Build Status	Coverage

Overview

Tulip is an open-source interior-point solver for linear optimization, written in pure Julia. It implements the homogeneous primal-dual interior-point algorithm with multiple centrality corrections, and therefore handles unbounded and infeasible problems. Tulip’s main feature is that its algorithmic framework is disentangled from linear algebra implementations. This allows to seamlessly integrate specialized routines for structured problems.

Installation

Just install like any Julia package

] add Tulip

Usage

The recommended way of using Tulip is through JuMP and/or MathOptInterface (MOI).

The low-level interface is still under development and is likely change in the future. The MOI interface is more stable.

Using with JuMP

Tulip follows the syntax convention PackageName.Optimizer:

using JuMP
import Tulip

model = Model(Tulip.Optimizer)

Linear objectives, linear constraints and lower/upper bounds on variables are supported.

Using with MOI

The type Tulip.Optimizer is parametrized by the model's arithmetic, e.g., Float64 or BigFloat. This allows to solve problem in higher numerical precision. See the documentation for more details.

import MathOptInterface
MOI = MathOptInterface
import Tulip

model = Tulip.Optimizer{Float64}()   # Create a model in Float64 precision
model = Tulip.Optimizer()            # Defaults to the above call
model = Tulip.Optimizer{BigFloat}()  # Create a model in BigFloat precision

Solver parameters

Setting parameters

When using Tulip through JuMP/MOI, parameters can be set either through MOI's generic OptimizerAttributes, e.g., MOI.TimeLimitSec and MOI.Silent, or by name.

• Through JuMP

  jump_model = JuMP.Model(Tulip.Optimizer)
  
  JuMP.set_optimizer_attribute(jump_model, "IPM_IterationsLimit", 200)

• Through MOI

  moi_model = Tulip.Optimizer{Float64}()
  
  MOI.set(moi_model, MOI.RawOptimizerAttribute("IPM_IterationsLimit"), 200)

• Through Tulip's API

  model = Tulip.Model{Float64}()
  
  Tulip.set_parameter(model, "IPM_IterationsLimit", 200)

Parameters description

See the documentation.

Command-line executable

See app building instructions.

Citing Tulip.jl

If you use Tulip in your work, we kindly ask that you cite the following reference (preprint available here).

@Article{Tulip.jl,
  author   = {Tanneau, Mathieu and Anjos, Miguel F. and Lodi, Andrea},
  journal  = {Mathematical Programming Computation},
  title    = {Design and implementation of a modular interior-point solver for linear optimization},
  year     = {2021},
  issn     = {1867-2957},
  month    = feb,
  doi      = {10.1007/s12532-020-00200-8},
  language = {en},
  url      = {https://doi.org/10.1007/s12532-020-00200-8},
  urldate  = {2021-03-07},
}