Articles on cvxoptdes

Example gallery

Sun, 18 Oct 2026 00:00:00 +0000

Optimization

Volcano height dataset

The volcano dataset included in the datasets R-package reports topographic information of the Maunga Whau (Mt Eden) volcano in the Auckland volcano field. To reduce the data grid size, we first downsample the volcano data, resulting in volcano heights across a $(44 \times 31)$ -dimensional matrix with rows corresponding to grid lines running east to west and columns to grid lines running south to north.

## initialize data
data(volcano)

## subsample grid
volcano <- volcano[c(TRUE, FALSE), c(TRUE, FALSE)]

data <- expand.grid(
 x1 = seq(from = -1, to = 1, length = dim(volcano)[1]),
 x2 = seq(from = -1, to = 1, length = dim(volcano)[2])
)
## standardize response
data[["y"]] <- (c(volcano) - min(volcano)) / (max(volcano) - min(volcano))

The irregular height response surface is not easily captured by a parametric linear or nonlinear model. Instead, a nonparametric regression model, such as a generalized additive model (GAM) or a Gaussian process regression (GPR) model, is better suited, allowing the complexity of the model to grow with the number of observations. In vignette("glm_gam_design"), the use of a GAM to model the volcano height was already discussed. In this example, we consider penalized design augmentation subject to a GPR prediction model, which is expected to behave similar to (multi-proposal) Bayesian Optimization. The objective is to maximize the observed height response, where the observed height at a specific grid point is assumed to be noise-free.

Generalized linear/additive model optimal design

Sun, 18 Oct 2026 00:00:00 +0000

Introduction

In vignette("lm_design"), the use of the lm_design R6-class is demonstrated to construct optimal designs for linear models. This vignette introduces the glm_design and gam_design R6-classes to calculate approximate and exact optimal designs for generalized linear and generalized additive models.

The methods available in the glm_design and gam_design classes are identical to those of the lm_design class, and it is recommended to read vignette("lm_design") before going through this vignette. The principal difference between optimal experiment design for generalized linear/additive models and linear models is that the information matrix of a generalized linear model is usually not independent of the model parameters $\boldsymbol{\theta}$ , similar to the information matrix of a nonlinear model, as explained in vignette("nlm_design").

Linear model optimal design

Sun, 18 Oct 2026 00:00:00 +0000

Getting started

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
data <- 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 = data ## design points
)

design$data
#> x1 x2 x3
#> 1 -2 -2 -1
#> 2 -1 -2 -1
#> 3 0 -2 -1
#> 4 1 -2 -1
#> 5 2 -2 -1
#> 6 -2 -1 -1
#> 7 -1 -1 -1
#> 8 0 -1 -1
#> 9 1 -1 -1
#> 10 2 -1 -1
....

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

Nonlinear/Linear mixed model optimal design

Sun, 18 Oct 2026 00:00:00 +0000

Nonlinear model optimal design

In vignette("lm_design"), the use of the lm_design R6-class is demonstrated to construct optimal designs for linear models. This vignette introduces the nlm_design and lme_design R6-classes to calculate approximate and exact optimal designs for nonlinear models and random intercept linear mixed models.

The methods available in the nlm_design class are largely equivalent to those in the lm_design class. The principal difference is that the information matrix of a nonlinear model $f$ is not independent of the model parameters $\boldsymbol{\theta}$ . Denote $F(\boldsymbol{x}_i, \boldsymbol{\theta})$ for the gradient vector of the nonlinear model $f$ with respect to the model parameters $\boldsymbol{\theta}$ evaluated at $\boldsymbol{x}_i$ , i.e. the $i$ -th row of the Jacobian matrix. Then, conditional on the error variance $\sigma_e^2$ , the $(p \times p)$ -information matrix is:

Optimal design augmentation

Sun, 18 Oct 2026 00:00:00 +0000

Introduction

In vignette("lm_design"), the implicit assumption is that the optimal design is calculated before observing the data. In practice, experimentation may take place in multiple consecutive steps, in which case it is desirable to construct a new augmented optimal design $\boldsymbol{w}^*$ given an initial (approximate or exact) design $\boldsymbol{w}_0 = (w_1^{(0)}, \ldots, w_{n}^{(0)})$ . Optimal design augmentation is supported by the $augment() method, which is demonstrated through several examples in this vignette.