Abstract <p>The paper gives a brief review of publications on clustering (grouping) of variables in modeling complex systems. In particular, we consider a universal variable-selection model that takes into account the possible roles for each variable; two methods for partitioning data into similar clusters and selecting informative variables that contribute to clustering; a new variable-selection method for use in cluster and classification analysis that is both intuitive and computationally efficient; a clustering procedure for mixed-type data using a latent-variable model; a regularization method for variable selection; and a method for clustering variables that is both intuitive and computationally efficient. Methods and object of the study: the object of the study is a simple nested piecewise linear regression, the right side of which includes an external minimum and internal minimum and maximum. The process of forming the sets of independent variables is based on the methods of linear regression analysis and the apparatus of mathematical programming. Results: the problem of identification of parameters of a simple nested piecewise linear regression of the first type, the right part of which includes an external minimum and internal minimum and maximum, as well as the formation of sets of independent variables for them, is formulated. The cases of both empty and non-empty intersection of the corresponding index sets are considered. The problem of minimizing the sum of approximation error modules arising in this case is reduced to a linear–Boolean programming problem. An illustrative example is solved.</p>