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.
nllsqimplements 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.
The following methods are provided for univariate functions:
Brent.fzeroimplements van Wijngaarden–Dekker–Brent method for finding a zero of a function (Brent, 1973).
Brent.fminimplements Brent's method for finding a minimum of a function (Brent, 1973).
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.maximize) implements the STEP method (Swarzberg et al., 1994) for finding the global minimum (resp. maximum) of a function on an interval.
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:
or from Julia by:
using Pkg Pkg.add(PackageSpec(url="https://github.com/emmt/OptimPackNextGen.jl.git"))
Rationale and related software
Related software are the
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
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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R.P. Brent, "Algorithms for Minimization without Derivatives," Prentice-Hall, Inc. (1973).
W.W. Hager & H. Zhang, "A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search," SIAM J. Optim., Vol. 16, pp. 170-192 (2005).
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M.J.D. Powell, "The BOBYQA Algorithm for Bound Constrained Optimization Without Derivatives", Technical report, Department of Applied Mathematics and Theoretical Physics, University of Cambridge (2009).
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