mixsqp: Fast maximum-likelihood estimation of mixture proportions using sequential quadratic programming

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The mixsqp R package provides algorithms based on sequential quadratic programming for maximum likelihood estimation of the mixture proportions in a finite mixture model where the component densities are known. The SQP algorithm is expected to obtain solutions that are at least as accurate as the state-of-the-art MOSEK interior-point solver (called via the “KWDual” function in the REBayes package), and is expected to compute these solutions much more quickly in large data sets.

For more details on the methods, please see the journal paper or the arXiv preprint.

The methods were originally implemented in Julia; please see here for the Julia implementation.

If you find a bug, or you have a question or feedback on our work, please post an issue.

Citing this work

If you find the mixsqp package or any of the source code in this repository useful for your work, please cite:

Youngseok Kim, Peter Carbonetto, Matthew Stephens and Mihai Anitescu. A fast algorithm for maximum likelihood estimation of mixture proportions using sequential quadratic programming. To appear in the Journal of Computational and Graphical Statistics.


Copyright (c) 2017-2020, Youngseok Kim, Peter Carbonetto, Matthew Stephens and Mihai Anitescu.

All source code and software in this repository are made available under the terms of the MIT license.

Quick Start

Install mixsqp from CRAN:


For more detailed installation instructions, see the “Setup” section below.

Once you have installed the package, load the package in R:


Next, run the small example provided with the mixsqp function:


For a more detailed illustration of the SQP algorithm applied to the problem of computing maximum-likelihood estimates for a mixture model, read through the introductory vignette.

To learn more, visit the package website, or view the “mixsqp” help page:



To install mixsqp from CRAN, in R run:


Alternatively, to install the latest version of the mixsqp package from GitHub, use devtools:

install_github("stephenslab/mixsqp",build_vignettes = TRUE)

This command should automatically install all required packages if they are not installed already.

If you have cloned the repository locally, you can install the package with the install_local function from devtools. Assuming your working directory contains the mixsqp repository, run this code to install the package:


Additional setup notes

devtools::install_github("stephenslab/mixsqp",build_vignettes = TRUE)

Developer notes

Testing the package

To install and test the mixsqp R package, run the following commands in the shell:

R CMD build mixsqp
R CMD INSTALL mixsqp_0.3-31.tar.gz
R CMD check --as-cran mixsqp_0.3-31.tar.gz

Note that these commands require that the dependencies have already been installed. See the DESCRIPTION file for details.

Updating the C++ source and documentation

When any changes are made to roxygen2 markup or to the C++ code in the src directory, simply run devtools::document() to update the RcppExports.cpp, the NAMESPACE file, and the package documentation files in the man directory.

Updating the pkgdown site

Run this line of R code to build the website (make sure you have an Internet connection while running the code):


Version 1.4.1 of pkgdown was used.

Other developer notes

Add file pre-commit to .git/hooks in the git repository to prevent commits that don’t include a change to the package version.


The mixsqp R package was developed by Youngseok Kim and Peter Carbonetto at the University of Chicago, with contributions from Matthew Stephens and Mihai Anitescu.