An almost pure Julia version of OptimPack for numerical optimization with particular focus on large scale problems
Author emmt
6 Stars
Updated Last
1 Year Ago
Started In
April 2017


License Build Status codecov.io

OptimPackNextGen is a Julia package for numerical optimization with particular focus on large scale problems.

Large scale problems

  • Quasi-Newton methods can be used to solve nonlinear large scale optimization problems. Optionally, bounds on the variables can be taken into account. The objective function must be differentiable and the caller must provide means to compute the objective function and its gradient.

  • Line searches methods are used to approximately minimize the objective function along a given search direction.

  • Algebra describes operations on "vectors" (that is to say the "variables" of the problem to solve).

Small to moderate size problems

For problems of small to moderate size, OptimPackNextGen provides:

  • Mike Powell's COBYLA (Powell, 1994), NEWUOA (Powell, 2006), and BOBYQA (Powell, 2009) algorithms for minimizing a function of many variables. These methods are derivatives free (only the function values are needed). NEWUOA is for unconstrained optimization. COBYLA accounts for general inequality constraints. BOBYQA accounts for bound constraints on the variables.

  • nllsq implements non-linear (weighted) least squares fit. Powell's NEWUOA method is exploited to find the best fit parameters of given data by a user defined model function.

Univariate functions

The following methods are provided for univariate functions:

  • Brent.fzero implements van Wijngaarden–Dekker–Brent method for finding a zero of a function (Brent, 1973).

  • Brent.fmin implements Brent's method for finding a minimum of a function (Brent, 1973).

  • Bradi.minimize (resp. Bradi.maximize) implements the BRADI ("Bracket" then "Dig"; Soulez et al., 2014) method for finding the global minimum (resp. maximum) of a function on an interval.

  • Step.minimize (resp. Step.maximize) implements the STEP method (Swarzberg et al., 1994) for finding the global minimum (resp. maximum) of a function on an interval.

Trust region

  • Methods gqtpar and gqtpar! implement Moré & Sorensen algorithm for computing a trust region step (Moré & D.C. Sorensen, 1983).


OptimPackNextGen can be installed from Julia package manager by the command:

add https://github.com/emmt/OptimPackNextGen.jl

or from Julia by:

using Pkg

Rationale and related software

Related software are the OptimPack library which implements the C version of the algorithms and the OptimPack.jl Julia package which is a wrapper of this library for Julia. Compared to OptimPack.jl, the new OptimPackNextGen.jl implements in pure Julia the algorithms dedicated to large scale problems but still relies on the C libraries for a few algorithms (notably the Powell methods). Precompiled versions of these libraries are provided by OptimPack_jll package. The rationale is to facilitate the integration of exotic types of variables for optimization problems in Julia. Eventually, OptimPackNextGen.jl will become the next version of OptimPack.jl but, until then, it is more flexible to have two separate modules and avoid coping with compatibility and design issues.


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  • E.G. Birgin, J.M. Martínez & M. Raydan, "Nonmonotone Spectral Projected Gradient Methods on Convex Sets," SIAM J. Optim. 10, 1196-1211 (2000).

  • R.P. Brent, "Algorithms for Minimization without Derivatives," Prentice-Hall, Inc. (1973).

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