Data and code underlying the publication: Diet optimization: modeling iron and zinc absorption by nonlinear programming and piecewise linear approximation using National Health and Nutrition Examination Survey

The aim of this study was to evaluate the effectiveness of nonlinear programming (NLP) and piecewise linear approximation (PLA) for solving diet models with nonlinear equations for nonheme iron and zinc absorption.

Please view https://doi.org/10.1016/j.ajcnut.2025.06.022 for added information on materials and methods.

- Meals and observed consumption
Meals and consumption data used for modeling were based on a.o. NHANES consumption data. The input data is further described in FolderContents - 1 Raw Data. The processing of the data was done in R, see FolderContents - 4 Model input data. This includes the estimation of food components such as phytate, which are necessary to estimate nonheme iron and zinc absorption.

- Estimation of absorbable iron and zinc
The formulas as described in literature were used to calculate the absorbable iron and zinc content of meals (see FolderContents - 2 Absorption equations).

- Piecewise linear approximation
For iron and zinc, univariate and bivariate piecewise linear approximation was performed, respectively (see FolderContents - 3 Piecewise linear approximation)

- Diet models
A mixed-integer and a continuous diet model were developed to optimize absorbable iron and zinc intake, using different absorption equations available from the literature (Conway and Hallberg for iron, and Miller for zinc). With the mixed-integer diet model, 3 types of 2-wk menu plans were created: omnivorous, vegetarian, and vegan. With the continuous diet model, diet plans were generated with a varying degree of allowed deviations from the observed diet. We tested the performance of NLP and PLA for both models. For NLP, 2 different nonlinear solvers were applied: LINDO and SCIP. In addition,  the efficiency of multistart and initialization functionalities and different time limits were tested (see FolderContents - 4 Diet model). 

- Processing and analysis scripts
All processing of data (modifications, calculations, etc.) and analysis of data was performed in R. All scripts are elaborately commented, describing each different step taken and the reason for the step.

- Figures and tables
All figures and tables were created through R. Refer to the R scripts for detailed information within the script.