cvxoptdes

An R-package for convex optimal experiment design, using exclusively open-source optimization solvers. cvxoptdes provides an object-oriented interface (using R6) to specify and optimize designs for linear models, generalized linear/additive models, nonlinear models, and random intercept linear mixed models. It supports optimization and augmentation of weighted, penalized and convex constrained approximate designs across a discrete grid of candidate points by solving a second-order cone program using the Splitting Cone Solver (SCS) and optimal rounding to integer-valued designs using point-exchange algorithms or mixed-integer programming with the HiGHS solver for orthogonally constrained designs. For details, see Chau et al. (2026).

Installation

When installing the R-package from source, verify that CMake is installed on the system and is found by R using e.g.,

Sys.which("cmake")
#>           cmake 
#> "/usr/bin/cmake"

With CMake available, install the R-package from source with:

## install.packages("remotes")
remotes::install_github("openanalytics/cvxoptdes")

Windows

Using Rtools42 or higher, CMake comes with the Rtools installation and is available by default.

Quick start

Optimal designs for linear models are calculated using the R6-class lm_design. When initializing a design object with lm_design$new(), the minimal required inputs are a (discrete) candidate design grid and a one-sided linear model formula:

library(cvxoptdes)

## 3 factors w/ 5, 5 and 3 levels
candidates <- expand.grid(
  x1 = -2:2,
  x2 = -2:2,
  x3 = -1:1
)

design <- lm_design$new(
  formula = ~(x1 + x2 + x3)^2 + I(x1^2) + I(x2^2) + I(x3^2),   ## full quadratic model
  data = candidates 
)

After initializing the linear model and design grid, use the $optimize() method to calculate an approximate optimal design:

design$optimize(criterion = "D")
#>  [1] 0.06 0.00 0.03 0.00 0.06 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.06 0.00 0.03 0.00 0.06 0.03 0.00 0.00 0.00
#> [30] 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.03 0.06 0.00 0.03 0.00 0.06 0.00 0.00 0.00
#> [59] 0.00 0.00 0.03 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.00 0.00 0.06 0.00 0.03 0.00 0.06
#> attr(,"criterion")
#> attr(,"criterion")$crit.value
#> [1] 1.897913
#> 
#> attr(,"criterion")$crit
#> [1] "D"

The $optimize() method returns the weights assigned to each design point in design$data, as well as the optimized value of the selected design criterion.

The $round() method then rounds the approximate optimal design to an exact (integer) design. If method = "optimal", repeated point-exchange procedures are executed to find the optimal exact design:

## parallel evaluation
mirai::daemons(n = parallel::detectCores() / 2, seed = 1)   

exact_design <- design$round(m = 13, method = "optimal", n_repeats = 100)

mirai::daemons(0)

exact_design
#>  [1] 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0
#> [74] 0 1
#> attr(,"criterion")
#> attr(,"criterion")$crit
#> [1] "D"
#> 
#> attr(,"criterion")$crit.value
#> [1] 1.84352
#> 
#> attr(,"criterion")$crit.rel.eff
#> [1] 0.9713409

design$subset(replicates = exact_design)
#>    x1 x2 x3
#> 1  -2 -2 -1
#> 5   2 -2 -1
#> 13  0  0 -1
#> 21 -2  2 -1
#> 25  2  2 -1
#> 28  0 -2  0
#> 36 -2  0  0
#> 50  2  2  0
#> 51 -2 -2  1
#> 55  2 -2  1
#> 65  2  0  1
#> 71 -2  2  1
#> 73  0  2  1

The existing lm_design object can be reused to compute optimal designs for other design criteria, or to evaluate other properties of a given design. For instance, the variance-covariance matrix of the linear model parameter estimates:

design$vcov(design_weights = exact_design, sigma2 = 1)
#>             (Intercept)     x1     x2     x3 I(x1^2) I(x2^2) I(x3^2)  x1:x2  x1:x3  x2:x3
#> (Intercept)       0.722 -0.002  0.002  0.005  -0.070  -0.070  -0.279  0.012  0.024 -0.024
#> x1               -0.002  0.025  0.000  0.000   0.001   0.000   0.000  0.000 -0.001  0.003
#> x2                0.002  0.000  0.025  0.000   0.000  -0.001   0.000  0.000  0.003 -0.001
#> x3                0.005  0.000  0.000  0.101   0.000   0.000  -0.006  0.003  0.001 -0.001
#> I(x1^2)          -0.070  0.001  0.000  0.000   0.030  -0.003  -0.014  0.000  0.000  0.008
#> I(x2^2)          -0.070  0.000 -0.001  0.000  -0.003   0.030  -0.014  0.000 -0.008  0.000
#> I(x3^2)          -0.279  0.000  0.000 -0.006  -0.014  -0.014   0.474 -0.015  0.000  0.000
#> x1:x2             0.012  0.000  0.000  0.003   0.000   0.000  -0.015  0.009  0.003 -0.003
#> x1:x3             0.024 -0.001  0.003  0.001   0.000  -0.008   0.000  0.003  0.035 -0.005
#> x2:x3            -0.024  0.003 -0.001 -0.001   0.008   0.000   0.000 -0.003 -0.005  0.035

Reference

Chau, J. and Segers, A. and Otava, M. and Karanja, S. (2026). “cvxoptdes: convex optimal experiment design in R.” doi:10.48550/arXiv.2610.14288. arXiv preprint.

Links

Learn more at https://repos.openanalytics.eu/docs/cvxoptdes/