960 Stars
Updated Last
1 Year Ago
Started In
April 2012


Univariate and multivariate optimization in Julia.

Optim.jl is part of the JuliaNLSolvers family.

For direct contact to the maintainer, you can reach out directly to pkofod on slack.

Documentation Build Status Social Reference to cite
Build Status JOSS
Build Status
Build Status
Codecov branch


Optim.jl is a package for univariate and multivariate optimization of functions. A typical example of the usage of Optim.jl is

using Optim
rosenbrock(x) =  (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
result = optimize(rosenbrock, zeros(2), BFGS())

This minimizes the Rosenbrock function

with a = 1, b = 100 and the initial values x=0, y=0. The minimum is at (a,a^2).

The above code gives the output

* Status: success

* Candidate solution
  Minimizer: [1.00e+00, 1.00e+00]
  Minimum:   5.471433e-17

* Found with
  Algorithm:     BFGS
  Initial Point: [0.00e+00, 0.00e+00]

* Convergence measures
  |x - x'|               = 3.47e-07 ≰ 0.0e+00
  |x - x'|/|x'|          = 3.47e-07 ≰ 0.0e+00
  |f(x) - f(x')|         = 6.59e-14 ≰ 0.0e+00
  |f(x) - f(x')|/|f(x')| = 1.20e+03 ≰ 0.0e+00
  |g(x)|                 = 2.33e-09 ≤ 1.0e-08

* Work counters
  Seconds run:   0  (vs limit Inf)
  Iterations:    16
  f(x) calls:    53
  ∇f(x) calls:   53

To get information on the keywords used to construct method instances, use the Julia REPL help prompt (?)

help?> LBFGS
search: LBFGS



  LBFGS(; m::Integer = 10,
  alphaguess = LineSearches.InitialStatic(),
  linesearch = LineSearches.HagerZhang(),
  precondprep = (P, x) -> nothing,
  manifold = Flat(),
  scaleinvH0::Bool = true && (typeof(P) <: Nothing))

  LBFGS has two special keywords; the memory length m, and
  the scaleinvH0 flag. The memory length determines how many
  previous Hessian approximations to store. When scaleinvH0
  == true, then the initial guess in the two-loop recursion
  to approximate the inverse Hessian is the scaled identity,
  as can be found in Nocedal and Wright (2nd edition) (sec.

  In addition, LBFGS supports preconditioning via the P and
  precondprep keywords.


  The LBFGS method implements the limited-memory BFGS
  algorithm as described in Nocedal and Wright (sec. 7.2,
  2006) and original paper by Liu & Nocedal (1989). It is a
  quasi-Newton method that updates an approximation to the
  Hessian using past approximations as well as the gradient.


    •    Wright, S. J. and J. Nocedal (2006), Numerical
        optimization, 2nd edition. Springer

    •    Liu, D. C. and Nocedal, J. (1989). "On the
        Limited Memory Method for Large Scale
        Optimization". Mathematical Programming B. 45
        (3): 503–528


For more details and options, see the documentation

  • STABLE — most recently tagged version of the documentation.
  • LATEST — in-development version of the documentation.


The package is a registered package, and can be installed with Pkg.add.

julia> using Pkg; Pkg.add("Optim")

or through the pkg REPL mode by typing

] add Optim


If you use Optim.jl in your work, please cite the following.

  author  = {Mogensen, Patrick Kofod and Riseth, Asbj{\o}rn Nilsen},
  title   = {Optim: A mathematical optimization package for {Julia}},
  journal = {Journal of Open Source Software},
  year    = {2018},
  volume  = {3},
  number  = {24},
  pages   = {615},
  doi     = {10.21105/joss.00615}