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A gradient-based outer approximation solver for convex mixed-integer nonlinear programming (MINLP)


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Pavito.jl is a mixed-integer convex programming (MICP) solver package written in Julia.

MICP problems are convex, except for restrictions that some variables take binary or integer values.

Pavito solves MICP problems by constructing sequential polyhedral outer-approximations of the convex feasible set, similar to Bonmin.

Pavito accesses state-of-the-art MILP solvers and continuous, derivative-based nonlinear programming (NLP) solvers through MathOptInterface.

For algorithms that use a conic solver instead of an NLP solver, use Pajarito. Pajarito is a robust mixed-integer conic solver that can handle such established problem classes as mixed-integer second-order cone programming (MISOCP) and mixed-integer semidefinite programming (MISDP).


Pavito.jl is licensed under the MPL 2.0 license.


Install Pavito using Pkg.add:

import Pkg

Use with JuMP

To use Pavito with JuMP, use Pavito.Optimizer:

using JuMP, Pavito
import GLPK, Ipopt
model = Model(
        "mip_solver" => optimizer_with_attributes(GLPK.Optimizer),
        "cont_solver" =>
            optimizer_with_attributes(Ipopt.Optimizer, "print_level" => 0),

The algorithm implemented by Pavito itself is relatively simple; most of the hard work is performed by the MILP solver passed as mip_solver and the NLP solver passed as cont_solver.

The performance of Pavito depends on these two types of solvers.

For better performance, you should use a commercial MILP solver such as CPLEX or Gurobi.


The following optimizer attributes can set to a Pavito.Optimizer to modify its behavior:

  • log_level::Int Verbosity flag: 0 for quiet, higher for basic solve info
  • timeout::Float64 Time limit for algorithm (in seconds)
  • rel_gap::Float64 Relative optimality gap termination condition
  • mip_solver_drives::Bool Let MILP solver manage convergence ("branch and cut")
  • mip_solver::MOI.OptimizerWithAttributes MILP solver
  • cont_solver::MOI.OptimizerWithAttributes Continuous NLP solver

Pavito is not yet numerically robust and may require tuning of parameters to improve convergence.

If the default parameters don't work for you, please let us know by opening an issue.

For improved Pavito performance, MILP solver integrality tolerance and feasibility tolerances should typically be tightened, for example to 1e-8.

Bug reports and support

Please report any issues via the GitHub issue tracker. All types of issues are welcome and encouraged; this includes bug reports, documentation typos, feature requests, etc. The Optimization (Mathematical) category on Discourse is appropriate for general discussion.


A gradient-based outer approximation solver for convex mixed-integer nonlinear programming (MINLP)







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